# How do you find the domain and range of f(x) = - sqrt ( 4x^2 + 2x^4 +5 )?

Jun 5, 2016

domain is $R$
range is all negative real numbers

#### Explanation:

under squareroot we can have a positive or zero number so
$2 {x}^{4} + 4 {x}^{2} + 5 \ge 0$
all the terms are positive because squared and summed
so it always is positive, for all x in R
because of squareroot produces a positive number and it is preceeded by negative sign, range is all negative real numbers