Define by . Which option correctly gives together with its…

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

Problem

Define f:(−∞,−1)∪(−1,∞)→Rf:\left(-\infty,-1\right)\cup(-1,\infty)\to\mathbb{R} by f(x)=2x−3x+1f(x)=\dfrac{2x-3}{x+1}. Which option correctly gives f−1(x)f^{-1}(x) together with its domain? (a) f−1(x)=x+3 x−2 ,  domain R∖{2}f^{-1}(x)=\dfrac{x+3}{\,x-2\,},\; \text{domain }\mathbb{R}\setminus\{2\} (b) f−1(x)=−x+3 x+2 ,  domain R∖{−2}f^{-1}(x)=-\dfrac{x+3}{\,x+2\,},\; \text{domain }\mathbb{R}\setminus\{-2\} (c) f−1(x)=−x+3 x−2 ,  domain R∖{2}f^{-1}(x)=-\dfrac{x+3}{\,x-2\,},\; \text{domain }\mathbb{R}\setminus\{2\} (d) f−1(x)=2x−3 x+1 ,  domain R∖{−1}f^{-1}(x)=\dfrac{2x-3}{\,x+1\,},\; \text{domain }\mathbb{R}\setminus\{-1\}

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