For the function defined by

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

Problem

For the function

f:\mathbb{R}\to\mathbb{R}

defined by

f(x)=3x-4

, answer the following. (i) Prove that

f

is bijective. (ii) Obtain the explicit expression for

f^{-1}

. (iii) Verify by direct substitution that

f^{-1}\circ f=I_{\mathbb{R}}

and

f\circ f^{-1}=I_{\mathbb{R}}

. (iv) Using the result of part (iii), solve the equation

f^{-1}\bigl(f(2x-1)\bigr)=5

for

x