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

\[\frac{ x^2 - 4 }{ x + 2 }\]

How many times does x go into x squared...?

and how many times does 2 go into -4...?

Answer 2

alternatively, you can factor the numerator using the difference of squares rule

Answer 3

Yes or as @jim_thompson5910 suggests

difference of square

x² + 4 = (x + 2)(x - 2)

Now you would have

\[\frac{ (x + 2)(x - 2) }{ x + 2 }\]

Notice how the (x + 2) would cancel out...and you would be left with...?

Answer 4

x-2?

Answer 5

Perfect!

Answer 6

Now the excluded value part.....this is asking...what number...will make your denominator = 0?

So

x + 2 = 0

what does x equal?

Answer 7

*this is called an excluded value...because if the denominator of a fraction...= 0 ...the function is "undefined"

Answer 8

So x =0? lol it wont let me msg you back. So thank you! I'm terrible with math

Answer 9

not quite

Your denominator.....is

x + 2

to find an excluded value...we need to set this to 0...and solve for x

x + 2 = 0


to solve for x....we need to isolate it...and subtract 2 from both sides...

x + 2 = 0
-2 -2

x = -2

Answer 10

Okay got it. thank you!

Answer 11

no problem :)