Question

3) Find the equation representing the inverse of the givenfunction. Check answer using your responses to previousproblems. (Type or insert picture of your work and final answer.)y = f(x) = 3x - 5

Answer 1

`f^(-1)(x)=(x)/(3)+(5)/(3)\text{ }`

1) To find the inverse function of a linear one, we must follow some steps:

2) Take the given function, and swap the variables so

`y=3x-5`

It's going to become in the process:

`x=3y-5`

3) And rewrite it putting y on the left side:

`\begin{gathered} -3y=-x-5 \\ 3y=x+5 \\ (3y)/(3)=(x)/(3)+(5)/(3) \\ y=(x)/(3)+(5)/(3)\text{ or} \\ f^(-1)(x)=(x)/(3)+(5)/(3)\text{ } \end{gathered}`

So that's our inverse function whose Range is the Domain of the original one and the Domain is the Range of the original one.