AP EAMCET · Maths · Differentiation
\(f: R \rightarrow R\) is a function such that \(f(0)=1\) and for all \(x, y \in R f(x y+1)=f(x) f(y)-f(y)\), \(-x+2\), then \(\frac{d f}{d x}\) at \(x=e\) is
- A 0
- B -1
- C \(e\)
- D 1
Answer & Solution
Correct Answer
(D) 1
Step-by-step Solution
Detailed explanation
Given functional relation is, \[ f(x y+1)=f(x) f(y)-f(y)-x+2 \] Now, put \(y=0\), then we are getting \[ \begin{gathered} f(\mathrm{l})=f(x) \cdot f(0)-f(0)-x+2 \\ \Rightarrow \quad f(\mathrm{l})=f(x)-1-x+2\{\because f(0)=1\} \end{gathered} \] On differentiating with respect to…
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