Consider the function given by .

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function g:R∖{75}→R∖{25}g: \mathbb{R}\setminus\left\{\dfrac{7}{5}\right\}\to\mathbb{R}\setminus\left\{\dfrac{2}{5}\right\} given by g(x)=2x+35x−7g(x)=\dfrac{2x+3}{5x-7}. (i) Show that gg is one–one. (ii) Show that gg is onto the stated codomain. (iii) Find g−1(x)g^{-1}(x) and state its domain and range. (iv) Prove that g(g−1(x))=x=g−1(g(x))g\bigl(g^{-1}(x)\bigr)=x=g^{-1}\bigl(g(x)\bigr) for all admissible xx.

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