Consider the function f: R 2 , , R 5

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function

f: \mathbb R\setminus\{2\}\,\longrightarrow\,\mathbb R\setminus\{5\},\qquad f(x)=\frac{5x+1}{x-2}.

(a) Prove that

f

is bijective between its stated domain and codomain. (b) Obtain an explicit formula for the function

g: \mathbb R\setminus\{5\}\,\longrightarrow\,\mathbb R\setminus\{2\}

which serves as the inverse of

f

. (c) Verify your result in part (b) by showing that

f\circ g

and

g\circ f

are both identity functions on their respective domains.