Cho hàm số y = f(x) = 3 4 x . Tính:
f(-5) | f(-4) | f(-1) | f(0) | f(1/2 ) |
f(1) | f(2) | f(4) | f(a) | f(a + 1) |
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1.
y=f(-1)=3*(-1)-2=-5
y=f(0)=3*0-2=-2
y=f(-2)=3*(-2)-2=-8
y=f(3)=3*3-2=7
Câu 2,3a làm tương tự,chỉ việc thay f(x) thôi.
3b
Khi y=5 =>5=5-2*x=>2*x=0=> x=0
Khi y=3=>3=5-2*x=>2*x=2=>x=1
Khi y=-1=>-1=5-2*x=>2*x=6=>x=3
f(-1)=3.1-2=3-2=1
f(0)=3.0-2=0-2=-2
f(-2)=3.(-2)-2=-6-2=-8
f(3)=3.3-2=9-2=7
\(a,f\left(1\right)=3\cdot1^2+1+1=5\\ f\left(-\dfrac{1}{3}\right)=3\cdot\left(-\dfrac{1}{3}\right)^2-\dfrac{1}{3}+1=\dfrac{1}{3}-\dfrac{1}{3}+1=1\\ f\left(\dfrac{2}{3}\right)=3\cdot\left(\dfrac{2}{3}\right)^2-\dfrac{2}{3}+1=\dfrac{4}{3}-\dfrac{2}{3}+1=\dfrac{5}{3}\\ f\left(-2\right)=3\cdot\left(-2\right)^2-2+1=11\\ f\left(-\dfrac{4}{3}\right)=3\cdot\left(-\dfrac{4}{3}\right)^2-\dfrac{4}{3}+1=\dfrac{16}{3}-\dfrac{4}{3}+1=5\)
\(b,f\left(\dfrac{2}{3}\right)=\left|2\cdot\dfrac{2}{3}-9\right|-3=\dfrac{23}{3}-3=\dfrac{14}{3}\\ f\left(-\dfrac{5}{4}\right)=\left|2\cdot\left(-\dfrac{5}{4}\right)-9\right|-3=\dfrac{23}{2}-3=\dfrac{17}{2}\\ f\left(-5\right)=\left|2\left(-5\right)-9\right|-3=19-3=16\\ f\left(4\right)=\left|2\cdot4-9\right|-3=1-3=-2\\ f\left(-\dfrac{3}{8}\right)=\left|2\cdot\left(-\dfrac{3}{8}\right)-9\right|-3=\dfrac{39}{4}-3=\dfrac{27}{4}\)
\(c,x=0\Rightarrow y=2\cdot0^2-7=-7\\ x=-3\Rightarrow y=2\cdot\left(-3\right)^2-7=11\\ x=-\dfrac{1}{2}\Rightarrow y=2\cdot\left(-\dfrac{1}{2}\right)^2-7=\dfrac{-13}{2}\\ x=\dfrac{2}{3}\Rightarrow y=2\cdot\left(\dfrac{2}{3}\right)^2-7=-\dfrac{55}{9}\)
Câu 1:
a)
\(y=f\left(x\right)=2x^2\) | -5 | -3 | 0 | 3 | 5 |
f(x) | 50 | 18 | 0 | 18 | 50 |
b) Ta có: f(x)=8
\(\Leftrightarrow2x^2=8\)
\(\Leftrightarrow x^2=4\)
hay \(x\in\left\{2;-2\right\}\)
Vậy: Để f(x)=8 thì \(x\in\left\{2;-2\right\}\)
Ta có: \(f\left(x\right)=6-4\sqrt{2}\)
\(\Leftrightarrow2x^2=6-4\sqrt{2}\)
\(\Leftrightarrow x^2=3-2\sqrt{2}\)
\(\Leftrightarrow x=\sqrt{3-2\sqrt{2}}\)
hay \(x=\sqrt{2}-1\)
Vậy: Để \(f\left(x\right)=6-4\sqrt{2}\) thì \(x=\sqrt{2}-1\)
Cho hàm số y = f(x) = 2x-3
a,Tính f(-2) ; f(-3/2) ; f(-3/4) ; f(0) ; f(1) ; f(1/2) ; f(5/2)
b,Lập bảng
a.f(-2)=2(-2)-3=(-7)
f(-3/2)=2.(-3/2)-3=(-6)
f(-3/4)=2.(-3/4)-3=(-3/2)-3=(-9/2)
f(0)=2.0-3=(-3)
f(1)=2.1-3=(-1)
f(1/2)=2.1/2-3=1-3=(-2)
f(5/2)=2.(5/2)-3=5-3=2
\(f\left(1\right)=3\cdot1^2+1+1=5\\ f\left(-\dfrac{1}{3}\right)=3\cdot\left(-\dfrac{1}{3}\right)^2-\dfrac{1}{3}+1=\dfrac{1}{3}-\dfrac{1}{3}+1=1\\ f\left(\dfrac{2}{3}\right)=3\cdot\left(\dfrac{2}{3}\right)^2+\dfrac{2}{3}+1=\dfrac{4}{3}+\dfrac{2}{3}+1=3\\ f\left(-2\right)=3\left(-2\right)^2-2+1=12-2+1=11\\ f\left(-\dfrac{4}{3}\right)=3\cdot\left(-\dfrac{4}{3}\right)^2-\dfrac{4}{3}+1=\dfrac{16}{3}-\dfrac{4}{3}+1=5\)
\(f\left(1\right)=3\cdot1^2+1+1=5\)
\(f\left(-\dfrac{1}{3}\right)=3\cdot\dfrac{1}{9}-\dfrac{1}{3}+1=1\)
\(f\left(\dfrac{2}{3}\right)=3\cdot\dfrac{4}{9}+\dfrac{2}{3}+1=3\)
a) Thay x=-2 vào hàm số f(x)=|3x-1|, ta được:
\(f\left(-2\right)=\left|3\cdot\left(-2\right)-1\right|=\left|-6-1\right|=7\)
Thay x=2 vào hàm số \(f\left(x\right)=\left|3x-1\right|\), ta được:
\(f\left(2\right)=\left|3\cdot2-1\right|=\left|6-1\right|=5\)
Thay \(x=-\dfrac{1}{4}\) vào hàm số \(f\left(x\right)=\left|3x-1\right|\), ta được:
\(f\left(-\dfrac{1}{4}\right)=\left|3\cdot\dfrac{-1}{4}-1\right|=\left|-\dfrac{3}{4}-\dfrac{4}{4}\right|=\dfrac{7}{4}\)
Thay \(x=\dfrac{1}{4}\) vào hàm số \(f\left(x\right)=\left|3x-1\right|\), ta được:
\(f\left(\dfrac{1}{4}\right)=\left|3\cdot\dfrac{1}{4}-1\right|=\left|\dfrac{3}{4}-1\right|=\dfrac{1}{4}\)
Vậy: f(-2)=7; f(2)=5; \(f\cdot\left(-\dfrac{1}{4}\right)=\dfrac{7}{4}\); \(f\left(\dfrac{1}{4}\right)=\dfrac{1}{4}\)
b) Để f(x)=10 thì \(\left|3x-1\right|=10\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=10\\3x-1=-10\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=11\\3x=-9\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{11}{3}\\x=-3\end{matrix}\right.\)
Để f(x)=-3 thì \(\left|3x-1\right|=-3\)
mà \(\left|3x-1\right|\ge0\forall x\)
nên \(x\in\varnothing\)