Question

7. Write the inverse of y = 1x + 10 given x < -10

Answer 1

• (a) x-10

,

• (b) (1-10x)/x

Step-by-step explanation:

Part A

Given the function:

`y=1x+10`

First, swap x and y:

`x=1y+10`

Next, make y the subject of the equation:

`y=x-10`

Therefore:

`f^(-1)(x)=x-10`

Part B

Given the function:

`y=(1)/(x+10)`

First, swap x and y:

`x=(1)/(y+10)`

Next, make y the subject of the equation:

`\begin{gathered} x=(1)/(y+10) \\ x(y+10)=1 \\ y+10=(1)/(x) \\ y=(1)/(x)-10 \\ y=(1-10x)/(x) \end{gathered}`

Therefore:

`f^(-1)(x)=(1-10x)/(x)`