COMEDK · Maths · 24. Functions
If \(f(x)=\frac{2 x-3}{3 x+4}\), then \(f^{-1}\left(\frac{-4}{3}\right)=\)
- A Zero
- B \(\frac{3}{4}\)
- C \(-\frac{2}{3}\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
\(f(x)=\frac{2 x-3}{3 x+4}\) Let \(f(x)=y=\frac{2 x-3}{3 x+4}\) On cross multiplication, we get \[ \begin{aligned} &3 x y+4 y=2 x-3 \\ &\Rightarrow \quad x(3 y-2)=-3-4 y \\ &\Rightarrow \quad x=\frac{-3-4 y}{3 y-2} \Rightarrow x=f^{-1}(y)=\frac{-3-4 y}{3 y-2} \end{aligned} \]…
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