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

##### 1 Answer

Domain:

Range:

#### 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

In your case, you have

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

This means that the domain of the function will be

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

Moreover, the denominator will **always** be positive, since you're dealing with a square. This means that the range of the function will be

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