AP EAMCET · Maths · Functions
If \(f(x)=\sqrt{x}-1\) and \(g\{f(x)\}=x+2 \sqrt{x}+1\) then \(g(x)=\)
- A \((x+2)^2\)
- B \((x-2)^2\)
- C \((\sqrt{x}+2)^2\)
- D \((\sqrt{x}-2)^2\)
Answer & Solution
Correct Answer
(A) \((x+2)^2\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\sqrt{x-1}\) and, \(g\{f(x)\}=x+2 \sqrt{x}+1=(\sqrt{x})^2+2 \sqrt{x}+1^2\) \(\Rightarrow g\{f(x)\}=(\sqrt{x}+1)^2\ldots\) (i) Let, \(f(x)=\sqrt{x}-1=t \Rightarrow \sqrt{x}=t+1\) By (i), \(g(\mathrm{t})=(\mathrm{t}+1+1)^2 \Rightarrow g(x)=(x+2)^2\)
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