Question

[Nguyễn Ngọc Nhã Hân]

Cho hai hàm số : \(f\left(x\right)=x^2\) và \(g\left(x\right)=3-x\)

a) Tính \(f\left(-3\right)\), \(f\left(-\dfrac{1}{2}\right)\), \(f\left(0\right)\), \(g\left(1\right)\), \(g\left(2\right)\), \(g\left(3\right)\)

b) xác định a để \(2f\left(a\right)=g\left(a\right)\)

Answer 1

[Akai Haruma]

Lời giải:

a)

\(f(-3)=(-3)^2=9; f(-\frac{1}{2})=(\frac{-1}{2})^2=\frac{1}{4}\)

\(f(0)=0^2=0\)

\(g(1)=3-1=2; g(2)=3-2=1; g(3)=3-3=0\)

b)

\(2f(a)=g(a)\)

\(\Leftrightarrow 2a^2=3-a\)

\(\Leftrightarrow 2a^2+a-3=0\Leftrightarrow (2a+3)(a-1)=0\)

\(\Rightarrow \left[\begin{matrix} a=\frac{-3}{2}\\ a=1\end{matrix}\right.\)