Question

Find the domain of the function

\(g\left( t \right) = \sqrt {3 - t} - \sqrt {2 + t} \)

Short answer

The domain of the function \(g\left( t \right) = \sqrt {3 - t} - \sqrt {2 + t} \)is\(\left( { - 2,\;3} \right)\).

Step-by-step solution

Describe the domain

The domain is the set of all values at which the given function is defined.

Find the domain of the function \(g\left( t \right) = \sqrt {3 - t}  - \sqrt {2 + t} \)

This is the square root function. So, first, find those values of \(t\) that make the radicand non-negative.

Solve\(3 - t\).

\(\begin{array}{c}3 - t \ge 0\\3 \ge t\end{array}\)

And,

Solve\(2 + t\).

\(\begin{array}{c}2 + t \ge 0\\t \ge - 2\end{array}\)

Put these values together to get\( - 2 \le t \le 3\).

Therefore, the domain of the function \(g\left( t \right) = \sqrt {3 - t} - \sqrt {2 + t} \)is\(\left( { - 2,\;3} \right)\).