Question

For the function g(x)= x-9/x+7, solve the following inequality. g(x)>_0

Answer 1

Answer:

$x< -7 ; x\geq9$

Step-by-step explanation:

You start noticing that for x = 9 g(x) =0, and for x= -7 the function isn't defined.

That splits the number lines in 3 areas: x<-7; -7<x<9, and x>9. (notice the strict inequalities since we already discussed the breaking points.

Let's try a point in each interval, namely, since i like the values, -10, 0, 10.

$g(-10) = \frac{-10-9}{-10+7} =\frac{-19}{-3} >0\\g(0) = \frac{0-9}{0+7}=-\frac{9}{7} 0$

We have all the informations we need. The value we need are $x< -7 ; x\geq9$