The function

f left parenthesis x right parenthesis equals x cubed minus 2f(x)=x3−2

is​ one-to-one.

a. Find an equation for

f Superscript negative 1f−1​,

the inverse function.

b. Verify that your equation is correct by showing that

f left parenthesis f Superscript negative 1 Baseline left parenthesis x right parenthesis right parenthesisff−1(x)equals=x

and

f Superscript negative 1 Baseline left parenthesis f left parenthesis x right parenthesis right parenthesisf−1(f(x))equals=x.

Question content area bottom

Part 1

a. Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Simplify your answer. Use integers or fractions for any numbers in the​ expression.)

A.

f Superscript negative 1 Baseline left parenthesis x right parenthesisf−1(x)equals=RootIndex 3 StartRoot x plus 2 EndRoot3x+2​,

for all x

Your answer is correct.

B.

f Superscript negative 1 Baseline left parenthesis x right parenthesisf−1(x)equals=enter your response here​,

for

xgreater than or equals≥enter your response here

C.

f Superscript negative 1 Baseline left parenthesis x right parenthesisf−1(x)equals=enter your response here​,

for

xless than or equals≤enter your response here

D.

f Superscript negative 1 Baseline left parenthesis x right parenthesisf−1(x)equals=enter your response here​,

for

xnot equals≠enter your response here

Part 2

b. Verify that the equation is correct.

f left parenthesis f Superscript negative 1 Baseline left parenthesis x right parenthesis right parenthesisff−1(x)

equals=

fleft parenthesis nothing right parenthesisenter your response here

and

f Superscript negative 1 Baseline left parenthesis f left parenthesis x right parenthesis right parenthesisf−1(f(x))

equals=

f Superscript negative 1 Baseline left parenthesis nothing right parenthesisf−1enter your response here

Substitute.

equals=

enter your response here

equals=

enter your response here

Simplify.