If a function $f : Q → R $ is defined by $f(x)=\frac{2x-1}{2}$ and $g : Q →  R$ is defined by $g(x)= x+2, $ then $(gof)(\frac{3}{2})$ is :

3

The correct answer is Option (4) → 3

$f : Q → R,f(x)=\frac{2x-1}{2}$

$g : Q →  R,g(x)= x+2$

$gof(x)=\frac{2x-1}{2}+2=\frac{2x-1+4}{2}$

$=\frac{2x+3}{2}$

$⇒gof\left(\frac{3}{2}\right)=\frac{2×\frac{3}{2}+3}{2}=\frac{6}{2}=3$