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

Decide whether or not the functions are inverses of each other.-example-1
User J Hunt
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1 Answer

1 vote

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.

User Kristen Balhoff
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