Question

If $f\left(g\right(x\left)\right)=g\left(f\right(x\left)\right)=x$ for all real numbers $x$ and $f\left(2\right)=5$ and $f\left(5\right)=3$, then the value of $g\left(3\right)+g\left(f\right(2\left)\right)$ is

• A. $7$
• B. $5$
• C. $3$
• D. $2$

Answer 1

Answer: (A)

$7$

Since $g$ and $f$ inverse, $g\left(3\right)=5$ and os
$g\left(3\right)+g\left(f\right(2\left)\right)=5+2=7$
$g^{-1}\left(x\right)=f\left(x\right);f^{-1}\left(x\right)=g\left(x\right)$
$f\left(2\right)=5$
$f^{-1}\left(5\right)=2;g\left(5\right)=2$

$f^{-1}\left(3\right)=5;g\left(3\right)=5$

$g\left(3\right)+g\left(f\right(2\left)\right)=g\left(3\right)+g\left(5\right)=7$