Question

True or False.The following function has an inverse.f(x) = -3x-7

Answer 1

Step 1

Given:

`f(x)\text{ = -3x-7}`

Required: To find if the function above has an inverse.

Step 2

Find the inverse

`\begin{gathered} \text{Let f(x) = y} \\ \text{Hence, y= -3x-7} \end{gathered}`

Replace x with y and y with x

`x=-3y-7`

Make y the subject of the formula

`\begin{gathered} x+7=-3y \\ (-3y)/(-3)=(x+7)/(-3) \end{gathered}`
`\begin{gathered} y=-((x+7))/(3) \\ f(x)\text{ =}-((x+7))/(3) \end{gathered}`

Hence, the function has an inverse, therefore the answer is true