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AP EAMCET · Maths · Functions

If \(f: R \rightarrow R, g: R \rightarrow \mathrm{R}\) are defined by \(f(x)=5 x-3, g(x)\) \(=x^2+3\), then \(g \circ f^{-1}(3)\) is equal to

  1. A \(\frac{25}{3}\)
  2. B \(\frac{111}{25}\)
  3. C \(\frac{9}{25}\)
  4. D \(\frac{25}{111}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{111}{25}\)

Step-by-step Solution

Detailed explanation

Given, \(f(x)=5 x-3\) and \(g(x)=x^2+3\) Let, \(y=f(x), \therefore y=5 x-3\) \[ \begin{aligned} & y+3=5 x \Rightarrow x=\frac{y+3}{5} \\ & \therefore f^{-1}(y)=\frac{y+3}{5} \Rightarrow f^{-1}(x)=\frac{x+3}{5} \end{aligned} \] Now, \(\quad g(x)=x^2+3\); So,…