AP EAMCET · Maths · Functions
If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are defined by \(f(x)=2 x+3\) and \(g(x)=x^2+7\), then the values of \(x\) such that \(g(x)=x^2+7\), then the values of \(x\) such that \(g(f(x))=8\) are
- A 1,2
- B \(-1,2\)
- C \(-1,-2\)
- D \(1,-2\)
Answer & Solution
Correct Answer
(C) \(-1,-2\)
Step-by-step Solution
Detailed explanation
we have, \(f(x)=2 x+3, g(x)=x^2+7\) \(g(f(x))=g(2 x+3)=(2 x+3)^2+7=8\) \(\Rightarrow \quad 4 x^2+9+12 x+7=8\) \(\Rightarrow \quad 4 x^2+12 x+8=0\) \(\Rightarrow \quad x^2+3 x+2=0\) \(\Rightarrow \quad(x+1)(x+2)=0\) \(\therefore \quad x=-1,-2\)
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