Solve the given problems related to the indicated examples of this section.

In Example 1, in the first line, change x² to −x². What other changes must be made in the rest of the paragraph?

Data from Example 1

The function f(x) = x² + 2 is defined for all real values of x. This means its domain is written as all real numbers. However, because x² is never negative, x² + 2 is never less than 2. We then write the range as all real numbers f(x) ≥ 2, where the symbol ≥ means “is greater than or equal to.”

The function

is not defined for t = −2, for this value would require division by zero. Also, no matter how large t becomes, f(t) will never exactly equal zero. Therefore, the domain of this function is all real numbers except −2, and the range is all real numbers except 0.

1 f(t) = + 1+2