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

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Answer 1 · 2018-01-25T08:37:55

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

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#