What does this mean? "For what values of x is f(x)>0?"

1 Answer
Jan 25, 2018

We want the values of x that give a y value greater than 0.

Explanation:

Let's say that f(x)=x^2-10

The graph below shows y=f(x):
graph{x^2-10 [-6, 6, -15, 15]}

When we want f(x)>0, we want y>0, or all the values of x where f(x)>0.

In this instance, x^2-10>0

x^2>10

x>sqrt(10)

x<-sqrt(10)

Proof:
x=10:
10^2-10=100-10=90

x=6
6^2-10=36-10=26

x=1:
1^2-10=1-10=-9

x=-1:
(-1)^2-10=1-10=-9

x=-6
(-6)^2-10=36-10=26

x=-10:
(-10)^2-10=100-10=90