Question

If $f:R\to R$ is defined by $f\left(x\right)=x^2-10x+21$ then $f^{-1}(-3)$ is

• A. $\{-4,6\}$
• B. $\{4,6\}$
• C. $\{-4,4,6\}$
• D. Not Invertible

Answer 1

The correct option is B $\{4,6\}$

Let $f^{-1}(-3)=t$
$\Rightarrow f\left(t\right)=-3$
$t^2-10t+21=-3$
$t^2-10t+24=0$
$t^2-6t-4t+24=0$
$t(t-6)-4(t-6)=0$
$\Rightarrow t=6,4=f^{-1}(-3)$