Question

Let g and f be two functions defined by

g(x)=(-5+x)(2+x)
f(x)=2-9x
for any real number x.
Find g/f(-3) and then find all values that are NOT in the domain of g/f. If there is more than one value, separate them with commas.
g/f(-3)= _________
Values that are NOT in the domain of g/f : ___________

Answer 1

g/f(-3) = (1/29) * (-5+x)(2+x)

2/9 is NOT in the domain of g/f

Explanation:

First we will calculate f(-3):

f(-3) = 2-9*(-3) = 2-(-27) = 2+27 = 29

Therefore, g/f(-3) = (1/29) * (-5+x)(2+x)

Now we will find the values that are not in the domain of g/f:

g/f = [(-5+x)(2+x)]/(2-9x)

The denominator of g/f should not be equal to zero, hence:

2-9x ≠ 0 ⇒ 2≠9x⇒x≠2/9

Therefore, 2/9 is NOT in the domain of g/f