Let f : N → R be the function defined by
Question:

Let $f: N \rightarrow R$ be the function defined by $f(x)=\frac{2 x-1}{2}$ and $g: Q \rightarrow R$ be another function defined by $g(x)=x+2$. Then, $(g \circ f)(3 / 2)$ is

(a) 1

(b) 2

(c) $\frac{7}{2}$

(d) none of these

Solution:

Given: $f(x)=\frac{2 x-1}{2}$ and $g(x)=x+2$

$(g o f)(x)=g(f(x))$

$=g\left(\frac{2 x-1}{2}\right)$

$=\frac{2 x-1}{2}+2$

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

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

$(g o f)\left(\frac{3}{2}\right)=\frac{2\left(\frac{3}{2}\right)+3}{2}$

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

$=\frac{6}{2}$

$=3$

​Hence, the correct option is (d).