Let be given by .

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

Problem

Let

f: \mathbb R \to \mathbb R

be given by

f(x)=3x-7

. (i) Find

f^{-1}(x)

. (ii) State the domains and the ranges of

f

and

f^{-1}

. (iii) Verify that

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

and

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

for all admissible

x

. Write the set of admissible values expressly in each case.

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