Question

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

Answer 1

Answer:

Given

• f(x) = 3 + 6x

A

Find the inverse of f(x):

• 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