JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f : R \rightarrow R\) be defined as \(f ( x )= x ^{3}+ x -5\). If \(g ( x )\) is a function such that \(f ( g ( x ))= x\), \(\forall x \in R\), then \(g ^{\prime}(63)\) is equal to
- A 0.02
- B 0.061
- C 0.88
- D 1.86
Answer & Solution
Correct Answer
(A) 0.02
Step-by-step Solution
Detailed explanation
\(f(x)=x^{3}+x-5\) \(\Rightarrow \quad f^{\prime}(x)=3 x^{2}+1 \Rightarrow\) increasing function \(\Rightarrow \quad\) invertible \(\Rightarrow \quad g(x)\) is inverse of \(f(x)\) \(\Rightarrow \quad g(f(x))=x\) \(\Rightarrow \quad g^{\prime}(f(x)) f^{\prime}(x)=1\)…
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