If $f(x)=\frac{3 x+4}{5 x-7}, x \neq \frac{7}{5}$ $g(x)=\frac{7 x+4}{5 x-3}, x \neq \frac{3}{5}$ then $(g…

If $f(x)=\frac{3 x+4}{5 x-7}, x \neq \frac{7}{5}$ $g(x)=\frac{7 x+4}{5 x-3}, x \neq \frac{3}{5}$ then $(g \circ f)(3)=$
  1. $-3$
  2. $-\frac{1}{3}$
  3. 3
  4. $\frac{1}{3}$

Solution

$\begin{aligned} \therefore(g \circ f)(x) &=g[f(x)] \\ &=g\left[\frac{3 x+4}{5 x-7}\right] \\ &=\frac{7\left(\frac{3 x+4}{5 x-7}\right)+4}{5\left(\frac{3 x+4}{5 x-7}\right)-3}=\frac{7(3 x+4)+4(5 x-7)}{5(3 x+4)-3(5 x-7)}=\frac{41 x}{41}=x \\ \therefore(g \circ f)(3) &=3 \end{aligned}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

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