Question

Let $f:N\to R$ be the function defined by $f\left(x\right)=\frac{2x-1}{2}\text{and}g:Q\to R$ be another function defined by $g\left(x\right)=x+2.$ Then $\left(gof\right)\frac{3}{2}$ is

• A. None of these
• B. $\frac{7}{2}$
• C. $1$
• D. $-1$

Answer 1

The correct option is A None of these

Find the value of composite function at given value.

Given: $f:N\to R\text{and}g:Q\to R$

Here, $f\left(x\right)=\frac{2x-1}{2}\&g\left(x\right)=x+2$

$\therefore gof\left(x\right)=g\left(f\right(x\left)\right)$

$=f\left(x\right)+2$

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

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

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


$\therefore gof\left(\frac{3}{2}\right)=3$

Hence, Option (d) is correct.