Question

How do you find the inverse of `h(x)=-3x+6` and is it a function?

Answer 1

The inverse function is `h^(-1)(x)=-1/3x+2`

Explanation:

To find the inverse function starting from `y=-3x+6` you have to calculate `x` in terms of `y`

`y=-3x+6`

`3x=-y+6`

`x=-1/3y+2`

Now we can write the inverse function returning to standard names of variables:

`h^(-1)(x)=-1/3x+2`

To find out if it is a function we have to find out if it fulfills 2 conditions:

1. it is defined for all values of `x`

2. It has different values for different argumants `x`

`h^(-1)` is a linear expression so it fulfills both conditions. This means it is a function.