Question

Decide whether or not the functions are inverses of each other.

Answer 1

Given the functions

`\begin{gathered} f(x)=3x+9 \\ g(x)=(1)/(3)x-3 \end{gathered}`

To decide whether or not the functions are inverses of each other,

Solving f(x) inversely i.e to give f⁻¹(x)

Where f(x) = y

`y=3x+9`

Replace y with x and x with y to give

`x=3y+9`

Solve for y i.e make y the subject

`\begin{gathered} x=3y+9 \\ 3y=x-9 \\ \text{Divide both sides by 3} \\ (3y)/(3)=(x-9)/(3) \\ y=(x)/(3)-(9)/(3) \\ y=(1)/(3)x-3 \end{gathered}`

The inverse of f(x) i.e f⁻¹(x) is

`f^(-1)(x)=(1)/(3)x-3`

From the above deductions, it can be seen that g(x) is the inverse of f(x), i.e g(x) = f⁻¹(x)

`g(x)=f^(-1)(x)=(1)/(3)x-3`

Thus, the functions are inverse of each other.

The answer is Yes.