Question

What is the range of `f(x) = 1 + sqrt(9 - x^2)`?

Answer 1

`1<=f(x)<=4`

Explanation:

The values that `f(x)` can take are dependent on the values for which `x` is defined.

So, in order to find the range of `f(x)`, we need to find its domain and take evaluate `f` at these points.

`sqrt(9-x^2)` is only defined for `|x| <=3`. But since we're taking the square of `x`, the smallest value it can take is `0` and the largest `3`.

`f(0) =4`

`f(3)=1`

Thus `f(x)` is defined over `[1,4]`.