Mathematics

Mathematics

Problem

Let

f:\mathbb R\to\mathbb R

be given by

f(x)=2x+3

and

g:\mathbb R\to\mathbb R

by

g(x)=\dfrac{x-3}{2}

. Which of the following statements is true? a)

g\circ f=x

but

f\circ g\neq x

, so

f

and

g

are not mutual inverses b) Both

f\circ g

and

g\circ f

equal

x

, so

f

and

g

are mutual inverses c)

f\circ g=x

but

g\circ f\neq x

, so

f

and

g

are not mutual inverses d) Both

f\circ g

and

g\circ f

simplify to

2x

, so

f

and

g

are not mutual inverses

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