Question

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

(b) 2

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

(d) none of these

Answer 1

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

$$\begin{gathered} \left(gof\right)\left(x\right)=g\left(f\left(x\right)\right) \\ =g\left(\frac{2x-1}{2}\right) \\ =\frac{2x-1}{2}+2 \\ =\frac{2x-1+4}{2} \\ =\frac{2x+3}{2} \\ \left(gof\right)\left(\frac{3}{2}\right)=\frac{2\left({\displaystyle \frac{3}{2}}\right)+3}{2} \\ =\frac{3+3}{2} \\ =\frac{6}{2} \\ =3 \end{gathered}$$

​Hence, the correct option is (d).

​