Question

Find the inverse of the one-to-one function. State the domain and the range of the inverse function.

Answer 1

So we have a function defined by 5 ordered pairs:

`\mleft\lbrace(7,-6),(-9,-10),(0,-3),(-6,2),(-10,-2)\mright\rbrace`

This means that the function takes five different x values and associate each of them with a y value. The inverse function exchanges x values with y values so the pairs that define it are those of f but with their coordinates interchanged. Then the inverse function is:

`\lbrace(-6,7),(-10,-9),(-3,0),(2,-6),(-2,-10)\rbrace`

And that's the first answer.

Then we need to find the domain of the inverse function. This is given by all the x values for which there's an associated y value. In other terms, the domain is composed of all the x values of the points that define the function. Ordering them from lowest to highest we get the domain of the inverse:

`\mleft\lbrace-10,-6,-3,-2,2\mright\rbrace`

And that's the second answer.