Question

Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x).
A. (g/f)(x) = x – 4, excluded value: x = -4.
B. (g/f)(x) = x – 2, excluded value: x = -2.
C. (g/f)(x) = x – 4, excluded value: x = 4.
D. (g/f)(x) = x – 2, excluded value: x = 2.

Answer 1

okay well we can factor g(x) to be (x+2)*(x-2)

Answer 2

so (g/f)(x) would be \[\frac{ (x+2)(x-2) }{ (x+2) }\]

Answer 3

so the (x+2) in the numerator and denominator cancel out, and you're left with x-2

Answer 4

so (g/f)(x) = x-2

Answer 5

but x cannot equal -2, because if x = -2, the denominator would be 0, and we cannot divide by 0

Answer 6

so your answer is B

Answer 7

Oh wow thank you! :)

Answer 8

you're welcome