Question

What is the domain and range of `g(x) = 1/(7-x)^2`?

Answer 1

Domain: `(-oo, 7) uu (7, + oo)`.
Range: `(0, +oo)`

Explanation:

The domain of the function will have to take into account the fact that the denominator cannot be equal to zero.

This means that any value of `x` that will make the denominator equal to zero will be excluded from the domain.

In your case, you have

`(7-x)^2 = 0 implies x = 7`

This means that the domain of the function will be `RR - {7}`, or `(-oo, 7) uu (7, + oo)`.

To find the range of the function, first note that a fractional expression can only be equal to zero if the numerator is equal to zero.

In your case, the numberator is constant and equal to `1`, which means that you cannot find an `x` for which `g(x) = 0`.

Moreover, the denominator will always be positive, since you're dealing with a square. This means that the range of the function will be `(0, +oo)`.

graph{1/(7-x)^2 [-20.28, 20.27, -10.14, 10.12]}