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2 years ago

8

Function Composition: Let the function

3+6x" alt="f(x)= 3+6x" align="absmiddle" class="latex-formula"> , determine:

1 answer:

V125BC [204]2 years ago

4 0

Answer:

<u>Given </u>

f(x) = 3 + 6x

A

<u>Find the inverse of f(x):</u>

x = 3 + 6f⁻¹(x)
6f⁻¹(x) = x - 3
f⁻¹(x) = (x - 3) / 6

B

f · f⁻¹( ∛5/6) =
f( f⁻¹( ∛5/6)) =
f((∛5/6 - 3)/6) =
3 + 6((∛5/6 - 3)/6) =
3 + ∛5/6 - 3 =
∛5/6

C

f · f⁻¹(x) =
f(f⁻¹(x)) =
f((x - 3)/6) =
3 + 6(x - 3)/6 =
3 + x - 3 =
x

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See below

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