Question

Suppose that the functions h and g are defined as follows.

h(x)=x−5

g(x)=(x+2)(x+3)

(a) Find (h/g)(−4).
(b) Find all values that are NOT in the domain of h/g

Answer 1

(h/g)(-4)

`((-4)-5)/((-4+2)(-4+3))`
Plug and chug
Should come out to be -4.5

`(x-5)/((x+2)(x+3))`
To find the values not in the domain, you must set each quantity in the denominator equal to zero and solve for x.
x+2=0 x+3=0
x≠-2 x≠-3
If x were either of these numbers, the denominator of the fraction would equal zero, which would give an undefined answer.