Question

If $f:R\to R$ is defined by $f(x)=x^2-6x-14,$ then $f^{-1}(2)$ equals to:

• A. {2, 8}
• B. $\{-2,8\}$
• C. $\{-2,-8\}$
• D. $\{2,-8\}$
• E. $\{\varphi \}$

Answer 1

Answer: (B)

Let $y=f(x)=x^2-6x-14$
$\Rightarrow$ $x^2-6x-14=2$
$\Rightarrow$ $x^2-6x-16=0$
$\Rightarrow$ $x^2-8x+2x-16=0$
$\Rightarrow$ $(x+2)(x-8)=0$
$\Rightarrow$ $x=\{-2,8\}$