Try the fastest way to create flashcards
Question

# Find the domain and range of the function. Write your answer in interval notation. $g(x)=\sqrt{16-x^{4}}$

Solution

Verified

Given function contains a square root. We must exclude all values of $x$ that give negative number in square root. In other words only $\textbf{positive}$ numbers (or zero) may occur in square root

Find the domain:

\begin{align*} 16-x^4&\geq 0\\ 16&\geq x^4\\ x^4 &\leq 16\\\\ x \leq 2&\text{ and } x\geq -2 \end{align*}

Thus, domain in interval notation is:

$\mathcal D_g =[-2,2]$

Square root function is increasing function, so to find its range we have to find minumum and maximum value of argument.

Minimum value is 0 when $x=-2$ or $x=2$ and maximum value is $16$ when $x=0$. Both these points are $\textbf{included}$ in the range.

Thus, range of function is $[\sqrt 0,\sqrt{16}]=[0,4]$.

## Recommended textbook solutions #### Biology

1st EditionISBN: 9780132013499Kenneth R. Miller, Levine
2,470 solutions #### Biology

1st EditionISBN: 9780133669510 (5 more)Kenneth R. Miller, Levine
2,590 solutions #### Miller and Levine Biology

1st EditionISBN: 9780328925124 (1 more)Joseph S. Levine, Kenneth R. Miller
1,773 solutions #### Biocalculus: Calculus for the Life Sciences

1st EditionISBN: 9781133109631 (1 more)Day, Stewart
5,056 solutions