# How do you find the domain & range for  g(t)= cos (1/t)?

Jan 29, 2016

Domain - all real numbers except zero.

The range is $- 1 \le g \left(t\right) \le 1$

#### Explanation:

The domain is the set of $x$ (or in this case $t$) values for which the function is valid.
In this case it doesn't matter how big or small $\frac{1}{t}$ gets, positively or negatively, as it will still form a valid angle as long as it is a real number. Therefore $\frac{1}{t}$ is only invalid when $t = 0$

Domain - all real numbers except zero.

The range is $- 1 \le g \left(t\right) \le 1$ as cosine is always in this range.