Mathematics

Problem

Consider the function

g: \mathbb{R}\setminus\left\{\dfrac{7}{5}\right\}\to\mathbb{R}\setminus\left\{\dfrac{2}{5}\right\}

given by

g(x)=\dfrac{2x+3}{5x-7}

. a. (i) Show that

g

is one–one. b. (ii) Show that

g

is onto the stated codomain. c. (iii) Find

g^{-1}(x)

and state its domain and range. d. (iv) Prove that

g\bigl(g^{-1}(x)\bigr)=x=g^{-1}\bigl(g(x)\bigr)

for all admissible

x