Choose the correct answer from the given four options.Let f : N R… - Vidyadip

MCQ

Choose the correct answer from the given four options.Let $f : N \rightarrow R$ be the function defined by $\text{f}(\text{x})=\frac{2\text{x}-1}{2}$ and $g : Q \rightarrow R$ be another function defined by $g(x) = x + 2.$ Then $(\text{gof})\frac{3}{2}$ is:

A
$1$
B
$1$
C
$\frac{7}{2}$
✓
None of these.

✓

Answer

Correct option: D.

None of these.

We have $\text{f}(\text{x})=\frac{2\text{x}-1}{2}$ and $g(x) = x + 2$
$\text{gof}\Big(\frac{3}{2}\Big)=\text{g}\Big(\text{f}\Big(\frac{3}{2}\Big)\Big)$
$=\text{g}\bigg(\frac{2\times\frac{3}{2}-1}{2}\bigg)$
$=\text{g}(1)=1+2=3$

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