Let f ∶ R → R be the function defined by f(x) = $\frac{2\mathrm{x}-1}{2}$ and g ∶ Q → R be another function defined by g(x) = x + 2. Then (g o f) $\frac{3}{2}$ is

Explanation:

Composition of function.

When the function f(x) is substituted in the function g(x), the composite function formed is represented by (g o f)x. It can be termed as “g of f of x".

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

We have f(x) = $\frac{2x-1}{2}$ and g(x) = x + 2.

Now, f($\frac{3}{2}$)=$\frac{2\times \frac{3}{2}-1}{2}$ = $\frac{2}{2}$ = 1

∴ (g o f)$\frac{3}{2}$ 

= g(f($\frac{3}{2}$))

= g(1)

= 1+2

= 3