If , where , then is equal…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

If f(x)=2x−1x+5f(x)=\frac{2x-1}{x+5}, where x≠−5x\ne-5, then f−1(x)f^{-1}(x) is equal to (a) x+52x−1\frac{x+5}{2x-1}, x≠12x\ne\frac{1}{2} (b) 5x+12−x\frac{5x+1}{2-x}, x≠2x\ne2 (c) 5x−12−x\frac{5x-1}{2-x}, x≠2x\ne2 (d) x−52x+1\frac{x-5}{2x+1}, x≠12x\ne\frac{1}{2}

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