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

Question

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

$1$
$1$
$\frac{7}{2}$
$\text{None of these}.$

✓

Answer

$\text{none of these}.$

Solution:
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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