Question

For questions 5&6 find F -1(x), the inverse of F(x)

Answer 1

To find the inverse function, we can follow the next steps:

First Function

1. Replace x with y as follows:

`y=3x+7\Rightarrow x=3y+7`

2. Solve the resulting equation for y. Subtract 7 from both sides of the equation:

`x-7=3y+7-7\Rightarrow x-7=3y`

3. Divide both sides of the equation by 3:

`((x-7))/(3)=(3)/(3)y\Rightarrow y=((x-7))/(3)=(1)/(3)(x-7)=(x)/(3)-(7)/(3)`Second Function

We need to repeat the process to obtain the inverse of this function:

1. Replace x with y:

`y=8x\Rightarrow x=8y`

2. Solve for y. Divide both sides by 8:

`(x)/(8)=(8)/(8)y\Rightarrow y=(x)/(8)`

In summary, we have that the inverse functions are:

For function

`y=3x+7`

The inverse function is:

`y=F^(-1)^{}(x)=((x-7))/(3)`

And, for the function

`y=8x`

The inverse function is:

`y=f^(-1)(x)=(1)/(8)x`