Q58 / 150 · MHT CET 2020 (14 Oct Shift 1) · Mathematics

If $f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$ then f of is

  • A
    an even function
  • B
    not defined for all $x \in R$
  • C
    a constant function
  • Correct answer
    D
    an odd function

Solution

We have, $\mathrm{f}(\mathrm{x})=\frac{2 \mathrm{x}+3}{3 \mathrm{x}-2}$ $\therefore(\mathrm{fof})(\mathrm{x})=\mathrm{f}[\mathrm{f}(\mathrm{x})]=\mathrm{f}\left(\frac{2 \mathrm{x}+3}{3 \mathrm{x}-2}\right)$ $=\frac{2\left(\frac{2 \mathrm{x}+3}{3 \mathrm{x}-2}\right)+3}{3\left(\frac{2 \mathrm{x}+3}{3 \mathrm{x}-2}\right)-2}=\frac{2(2 \mathrm{x}+3)+3(3 \mathrm{x}-2)}{3(2 \mathrm{x}+3)-2(3 \mathrm{x}-2)}$ $=\frac{4 \mathrm{x}+6+9 \mathrm{x}-6}{6 \mathrm{x}+9-6 \mathrm{x}+4}=\frac{13 \mathrm{x}}{13}=\mathrm{x} \quad \ldots$ is an odd function

Hence, the correct answer is option: 'D'.

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