# Math Help - Function inequality

1. ## Function inequality

Solve the following inequality for the given function f(x):

f(x) = (x^2 + 1)(-2 - 3x^2)

a. f(x) > 0
b. f(x) ≥ 0
c. f(x) < 0
d. f(x) ≤ 0

Thank you for any help, I appreciate it!

2. Here is a hint
x²+1 > 0 for all x real
3x² + 2 > 0 for all x real

3. Do I graph the function and take the answers from the graph?

4. No 'cause running-gag's hint is the best hint you'd ever get.

$f$ is $-\left( x^{2}+1 \right)\left( 3x^{2}+2 \right),$ and those factors are always positive, hence $f<0$ for all $x.$