{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-2"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["sqrt","x_sqrt","frac","sqr","x_"],"ques":"Cho h\u00e0m s\u1ed1 $ f(x) = \\dfrac{2}{x-1} .$ T\u00ecm $x$ sao cho $f(x) = \\dfrac{-2}{3} ?$ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x = $ _input_ ","explain":"Ta c\u00f3: $ f(x) = \\dfrac{-2}{3} \\\\ \\Rightarrow \\dfrac{2}{x-1} = \\dfrac{-2}{3} \\\\ \\Rightarrow \\begin{cases} x \\neq 1 \\\\ 6 = -2(x-1) \\end{cases} \\\\ \\Rightarrow \\begin{cases} x \\neq 1 \\\\ 6 = -2x + 2 \\end{cases} \\\\ \\Rightarrow \\begin{cases} x \\neq 1 \\\\ -2x = 4 \\end{cases} \\\\ \\Rightarrow \\begin{cases} x \\neq 1 \\\\ x = -2 \\end{cases} $ <br\/><br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $x = -2$ <\/span><\/span> "}]}],"id_ques":701},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","t","f","f"]],"list":[{"point":10,"image":"","content":"","col_name":["Cho h\u00e0m s\u1ed1 $y = f(x) = \\dfrac{1}{4}x^{3} $","\u0110\u00fang","Sai"],"arr_ques":[" $f(-2) = -2 $"," $f(-1) = \\dfrac{-1}{4} $","$f(0) = \\dfrac{1}{2} $"," $f(3) = \\dfrac{3}{4} $"],"explain":[" V\u1edbi $x=-2$ th\u00ec $f(-2) = \\dfrac{1}{4}.(-2)^{3} = \\dfrac{1}{4}.(-8) = -2 $","<br\/>V\u1edbi $x=-1$ th\u00ec $f(-1) = \\dfrac{1}{4}.(-1)^{3} = \\dfrac{-1}{4} $","<br\/> V\u1edbi x = 0 th\u00ec $f(0) = \\dfrac{1}{4}.0^{3} = 0 $ ","<br\/> V\u1edbi x = 3 th\u00ec $f(3) = \\dfrac{1}{4}.(3)^{3} = \\dfrac{1}{4}.27= \\dfrac{27}{4} $"]}]}],"id_ques":702},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["-8"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" Cho h\u00e0m s\u1ed1 $y = f(x) = (a+2)x + 2a + 5 .$ T\u00ecm a bi\u1ebft $f(-3) = 7 ? $ <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $a = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$","explain":" Ta c\u00f3: $y = (a+2)x + 2a + 5 $ <br\/> Do \u0111\u00f3: $f(-3) $ $ = (a+2).(-3) + 2a + 5 \\\\ = -3a - 6 + 2a + 5 \\\\ = -a - 1 $ <br\/> M\u00e0 $f(-3) = 7 \\\\ \\Rightarrow -a - 1 = 7 \\\\ \\Rightarrow -a = 8 \\\\ \\Rightarrow a = -8 $ <br\/><br\/><span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $-8$ <\/span><\/span> "}]}],"id_ques":703},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" Cho h\u00e0m s\u1ed1: $f(x) = ax^{2} + bx + c .$ Bi\u1ebft $f(0) = 3; f(1) = 0; f(-1) = 1.$ T\u00ecm $a, b, c ?$ ","select":["A. $a = \\dfrac{-5}{2}, b = \\dfrac{-1}{2}, c = 3 $","B. $a = \\dfrac{-1}{2}, b = \\dfrac{-5}{2}, c = 3 $","C. $a = -3 , b = 1, c = 3 $ ","D. $a = 3, b = 1, c = 0 $"],"explain":" Ta c\u00f3: $f(x) = ax^{2} + bx + c $ <br\/> Do \u0111\u00f3: $ f(0) = a.0 + b.0 + c = c \\\\ f(1) = a.1^{2} + b.1 + c = a + b + c \\\\ f(-1) = a.(-1)^{2} + b.(-1) + c = a - b + c $ <br\/> M\u00e0 $f(0) = 3; f(1) = 0; f(-1) = 1$ <br\/> $\\Rightarrow \\begin{cases} c = 3 \\\\ a + b + c = 0 \\\\ a - b + c = 1 \\end{cases} $$ \\Rightarrow \\begin{cases} c = 3 \\\\ a + b = -3 \\\\ a - b = -2 \\end{cases} $$ \\Rightarrow \\begin{cases} c = 3 \\\\ a = \\dfrac{-5}{2} \\\\ b = \\dfrac{-1}{2} \\end{cases}$<br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":704},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" Cho h\u00e0m s\u1ed1: $y = f(x) = \\begin{cases} x + 2 \\text { v\u1edbi } x \\geq -2 \\\\ -x - 2 \\text { v\u1edbi } x < -2 \\end{cases} .$ T\u00ecm $x$ \u0111\u1ec3 $f(x) = \\dfrac{-1}{2}? $","select":["A. $ x = \\dfrac{-5}{2} $","B. $ x = \\dfrac{-3}{2} $","C. $ x = \\varnothing $","D. $ x = \\pm \\dfrac{1}{2} $"],"hint":"- Vi\u1ebft bi\u1ec3u th\u1ee9c x\u00e1c \u0111\u1ecbnh f(x). <br\/> Cho f(x) = $\\dfrac{-1}{2}$ r\u1ed3i t\u00ecm x. ","explain":" Bi\u1ec3u th\u1ee9c x\u00e1c \u0111\u1ecbnh f(x) l\u00e0: $y = f(x) = |x + 2| $ <br\/> $f(x) = \\dfrac{-1}{2} \\Leftrightarrow |x + 2| = \\dfrac{-1}{2} $ (v\u00f4 l\u00fd) (V\u00ec $|x + 2| \\geq 0 $) <br\/> V\u1eady kh\u00f4ng c\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a $x$ \u0111\u1ec3 $f(x) = \\dfrac{-1}{2} $ <br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":705},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" Trong c\u00e1c t\u01b0\u01a1ng quan sau t\u01b0\u01a1ng quan n\u00e0o l\u00e0 t\u01b0\u01a1ng quan h\u00e0m s\u1ed1? <br\/> H\u00ecnh 1<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai15/lv3/img\/D7C23-03.png' \/><\/center> H\u00ecnh 2 <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai15/lv3/img\/D7C23-04.png' \/><\/center> ","select":["A. H\u00ecnh 1","B. H\u00ecnh 2","C. H\u00ecnh 1 v\u00e0 H\u00ecnh 2","D. Kh\u00f4ng c\u00f3 h\u00ecnh n\u00e0o"],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/> <b> C\u1ea7n ki\u1ec3m tra \u0111i\u1ec1u ki\u1ec7n: <\/b> <br\/> M\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a \u0111\u1ea1i l\u01b0\u1ee3ng $x$ \u0111\u01b0\u1ee3c t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t v\u00e0 ch\u1ec9 m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee7a \u0111\u1ea1i l\u01b0\u1ee3ng $y$ hay kh\u00f4ng? <\/span> <br\/><br\/><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> <br\/><span class='basic_left'> X\u00e9t h\u00ecnh 1, c\u00f3 f l\u00e0 h\u00e0m s\u1ed1 t\u1eeb X \u0111\u1ebfn Y v\u00ec m\u1ed7i gi\u00e1 tr\u1ecb c\u1ee7a $x \\in X $ \u0111\u01b0\u1ee3c t\u01b0\u01a1ng \u1ee9ng v\u1edbi m\u1ed9t v\u00e0 ch\u1ec9 m\u1ed9t gi\u00e1 tr\u1ecb c\u1ee7a $y \\in Y$. <br\/> X\u00e9t h\u00ecnh 2, g kh\u00f4ng ph\u1ea3i l\u00e0 h\u00e0m s\u1ed1 v\u00ec X kh\u00f4ng ph\u1ea3i l\u00e0 t\u1eadp h\u1ee3p s\u1ed1. <\/span> <br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":706},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"],["0"]]],"list":[{"point":10,"width":50,"type_input":"","ques":" Cho h\u00e0m s\u1ed1: $y = f(x) = \\begin{cases} 0,5x - 3 \\text { n\u1ebfu } x \\geq 6 \\\\ 3 - 0,5x \\text { n\u1ebfu} x < 6 \\end{cases} $ <br\/> Khi \u0111\u00f3: $f(-2) = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} \\\\ f(6) = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$","hint":"X\u00e9t d\u1ea5u c\u1ee7a $x$ \u0111\u1ec3 t\u00ednh $f(x)$.","explain":" V\u1edbi $x = -2 < 6 $ th\u00ec $f(x) = 3 - 0,5x $ <br\/> $ \\Rightarrow f(-2) = 3 - 0,5.(-2) = 3 + 1 = 4 $ <br\/> V\u1edbi $x = 6 $ th\u00ec $f(x) = 0,5x - 3$ <br\/> $\\Rightarrow f(6) = 0,5.6 - 3 = 3 - 3 = 0 $ <br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 4; 0. <\/span><\/span> "}]}],"id_ques":707},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" Bi\u1ebft $f(x) = (1-x).f(x-1)$ v\u1edbi $x > 1$ <br\/> T\u00ednh $f(4)$ n\u1ebfu $f(1) = 1?$ ","select":["A. $f(4) = -9$","B. $f(4) = -3 $","C. $f(4) = -6$","D. $f(4) = -1 $"],"hint":"T\u00ednh l\u1ea7n l\u01b0\u1ee3t f(2), f(3), f(4)","explain":" Ta c\u00f3: $f(x) = (1-x).f(x-1)$ <br\/> Do \u0111\u00f3: $f(2) = (1-2).f(2-1) = -1.f(1) = -1.1 = -1 \\\\ f(3) = (1-3).f(3-1) = -2.f(2) = -2.(-1) = 2 \\\\ f(4) = (1-4).f(4-1) = -3.f(3) = -3.2 = -6$ <br\/> V\u1eady $f(4) = -6$ <br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":708},{"time":24,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["4"]]],"list":[{"point":10,"width":50,"type_input":"","input_hint":["sqrt","x_sqrt","frac","sqr","x_"],"ques":"Cho h\u00e0m s\u1ed1 $y = f(x) = \\dfrac{2}{x} $ <br\/> Khi \u0111\u00f3: $f\\left(-1\\dfrac{2}{3} \\right).f\\left(\\dfrac{1}{-1\\dfrac{2}{3}} \\right) $ = _input_ ","explain":" Ta c\u00f3: $y = \\dfrac{2}{x}$ <br\/> Do \u0111\u00f3: $f\\left(-1\\dfrac{2}{3} \\right).f\\left(\\dfrac{1}{-1\\dfrac{2}{3}} \\right) \\\\ = \\dfrac{2}{-1\\dfrac{2}{3}}.\\dfrac{2}{\\dfrac{1}{-1\\dfrac{2}{3}}}\\\\ = \\dfrac{2}{-1\\dfrac{2}{3}}.\\left[2.\\left( -1\\dfrac{2}{3}\\right) \\right] \\\\ = 2 . 2 \\\\ = 4 $<\/span> "}]}],"id_ques":709},{"time":14,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" Cho h\u00e0m s\u1ed1 $y = f(x) = 2x^{2} + 3 $ v\u00e0 $f(a) = 21.$ Khi \u0111\u00f3 gi\u00e1 tr\u1ecb c\u1ee7a a b\u1eb1ng: ","select":["A. $a = -3 $","B. $a = 3 $","C. $a = 3 $ ho\u1eb7c $a = -3 $","D. $a \\neq \\pm 3$"],"explain":" Ta c\u00f3: $y = f(x) = 2x^{2} + 3 $ <br\/> Do \u0111\u00f3 $f(a) $ $ = 2a^{2} + 3 = 21 \\\\ \\Rightarrow 2a^{2} = 18 \\\\ \\Rightarrow a^{2} = 9 \\\\ \\Rightarrow a = \\pm 3 $ <br\/><br\/><span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":710}],"lesson":{"save":0,"level":3}}