Question

For question 4 find F -1 (x), the inverse of F(x)

Answer 1

F⁻¹(x) = 6(x - 3)

Step-by-step explanation

To find the inverse function we have to clear x as a function of f. In this function

`F(x)=(x)/(6)+3`

the first step is to subtract 3 from both sides of the equation:

`\begin{gathered} F(x)-3=(x)/(6)+3-3 \\ F(x)-3=(x)/(6) \end{gathered}`

And then multiply both sides by 6:

`\begin{gathered} 6(F(x)-3)=(x)/(6)\cdot6 \\ 6(F(x)-3)=x \end{gathered}`

Finally change the names of x and F(x). x is now F⁻¹(x) and F(x) is now x:

`F^(-1)(x)=6(x-3)`