Question

Find the values of x for which the combined function h(x)=f(x)/g(x) is undefined if f(x)=5x+1 and g(x)=x^2-9

Answer 1

Answer:

We need to know the definition of the "combined function" h(x). I'm going to guess--by looking at answers--that the function is h(x)=\frac{f(x)}{g(x)}h(x)=

g(x)

f(x)

making it

h(x)=\frac{5x+1}{x^2-9}h(x)=

x

2

−9

5x+1

This function is undefined wherever the denominator is equal to 0 (division by zero is undefined). Factor the denominator.

h(x)=\frac{5x+1}{(x+3)(x-3)}h(x)=

(x+3)(x−3)

5x+1

The two values of x that make the denominator 0 are 3 and -3, otherwise written x=\pm 3x=±3