Let the function f be defined by f(x)=\(\frac{9+3x}{7-2x}\), then f^-1(x) is ______(a) \(\frac{9-3x}{7+2x}\)(b) \(\frac{7x-9}{2x+3}\)(c) \(\frac{2x-7}{3x+9}\)(d) \(\frac{2x-3}{7x+9}\)This question was addressed to me during an online interview.This key question is from Composition of Functions and Invertible Function in section Relations and Functions of Mathematics – Class 12

Let the function f be defined by f(x)=\(\frac{9+3x}{7-2x}\), then f^-1

1.	Let the function f be defined by f(x)=\(\frac{9+3x}{7-2x}\), then f^-1(x) is ______(a) \(\frac{9-3x}{7+2x}\)(b) \(\frac{7x-9}{2x+3}\)(c) \(\frac{2x-7}{3x+9}\)(d) \(\frac{2x-3}{7x+9}\)This question was addressed to me during an online interview.This key question is from Composition of Functions and Invertible Function in section Relations and Functions of Mathematics – Class 12
Answer» RIGHT answer is (b) \(\frac{7x-9}{2x+3}\) To EXPLAIN I would say: The FUNCTION f(X)=\(\frac{9+3x}{7-2x}\) is bijective. ∴ f(x)=\(\frac{9+3x}{7-2x}\) i.e.y=\(\frac{9+3x}{7-2x}\) 7y-2xy=9+3x 7y-9=x(2y+3) x=\(\frac{7y-9}{2y+3}\) ⇒f^-1 (x)=\(\frac{7y-9}{2x+3}\).

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