Mathematics - Functions Question with Solution | TestHub

Given, $f(x)=5x-3$ and $g(x)=x^2+3$ Let, $y=f(x),\therefore y=5x-3$ $y+3=5x\Rightarrow x=\frac{y+3}{5}$ $\therefore f^{-1}(y)=\frac{y+3}{5}\Rightarrow f^{-1}(x)=\frac{x+3}{5}$ Now, $g(x)=x^2+3$ So, $g\circ f^{-1}(3)=g\left[f^{-1}(3)\right]$ $=g\left(\frac{3+3}{5}\right)=g\left(\frac{6}{5}\right)=\frac{(6{)}^2}{(5{)}^2}+3=\frac{36}{25}+3=\frac{111}{25}$