MHT CET · Maths · Functions
If a function \(f: R \rightarrow R\) is defined by \(f(x)=\frac{4 x}{5}+3\), then \(f^{-1}(x)=\)
- A \(\frac{5(x+3)}{4}\)
- B \(\frac{5(x-3)}{4}\)
- C \(\frac{4(x+3)}{5}\)
- D \(\frac{4(x-3)}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{5(x-3)}{4}\)
Step-by-step Solution
Detailed explanation
(A)
Let \(f(x)=\frac{4 x}{5}+3=y\)
\(\therefore 4 x=5 y-15 \Rightarrow x=\frac{5 y-15}{4}\)
\(\therefore f^{-1}(y)=\frac{5 y-15}{4} \Rightarrow f^{-1}(x)=\frac{5 x-15}{4}=\frac{5(x-3)}{4}\)
Let \(f(x)=\frac{4 x}{5}+3=y\)
\(\therefore 4 x=5 y-15 \Rightarrow x=\frac{5 y-15}{4}\)
\(\therefore f^{-1}(y)=\frac{5 y-15}{4} \Rightarrow f^{-1}(x)=\frac{5 x-15}{4}=\frac{5(x-3)}{4}\)
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