Question

Let $f\left(x\right)=\frac{3}{2}+\sqrt{x-\frac{3}{4}}$ be a function and $g\left(x\right)$ be another function such that $g\left(f\left(x\right)\right)=x,$ then the value of $g\left(20\right)$ will be

• A. $333$
• B. $335$
• C. $338$
• D. $343$

Answer 1

The correct option is D $343$

$g\left(x\right)$ is inverse of $f\left(x\right)$

$\Rightarrow$ $x=\frac{3}{2}+\sqrt{y-\frac{3}{4}}$

$\Rightarrow$ $y={(x-\frac{3}{2})}^2+\frac{3}{4}=f^{-1}\left(x\right)=g\left(x\right)$

$\therefore$ $g\left(20\right)={(20-\frac{3}{2})}^2+\frac{3}{4}=343$