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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
MCQ
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:
  • A
    $1$
  • B
    $1$
  • C
    $\frac{7}{2}$
  • ✓
    $\text{None of these}.$
✓

Answer

Correct option: D.
$\text{None of these}.$
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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