For real constants and

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

Problem

For real constants

k>0,\ m\neq 0

and

c\in\mathbb R

, define

f:\mathbb R\to(c,\infty)

by

f(x)=k e^{mx}+c

. (i) Verify that

f

is injective. (ii) Obtain an explicit formula for

f^{-1}(y)

in terms of

k,\ m,

and

c

. State the domain and range of

f^{-1}

. (iii) If

k=3,\ m=2,\ c=1

, evaluate

f^{-1}(7)

.

Related theory

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