How do you find the domain and range of g(t) = 5t?

Mar 24, 2017

See explanation.

Explanation:

Domain

The domain is the largest subset of real numbers $\mathbb{R}$ for which the function is defined. To find it we have to look for any possible values of $x$ for which the function is undefined.

The possible exclusions are:

• zeroes of denominators,

• values for which expressions under square root sign (or other roots with an even degree) are negative

• values for which expressions under logarythm signs are negative or zero

The given function does not contain any of the limitations mentioned above, therfore its domain is $\mathbb{R}$

Range

To find the range we have to look for possible values of the function. From the formula we see that the values can be all numbers in $\mathbb{R}$. As the arguments go to minus infinity, the values also go to minus infinity. The situation is simmilar when $x$ goes to plus infinity. The values also grow up to plus infinity.
So the range is also $\mathbb{R}$