Let be defined by

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

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

be defined by

f(x)=3x-5

. Answer the following. (i) Determine the set of values taken by

f

(range). (ii) Obtain the expression of the inverse function

f^{-1}

and write its domain and range. (iii) Verify that

f\bigl(f^{-1}(y)\bigr)=y

for all permissible

y

. (iv) Verify that

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

for all real

x

. Explain why these results confirm that

f^{-1}

obtained in part (ii) is indeed the inverse of

f