SOLUTION: If F(x) = 3x^2 - 5x and G(x) = 2x - 4, find G of F(2) and F of G(2) I'm having trouble with this problem. Any help is appreciated. Thanks.

Algebra ->  Functions -> SOLUTION: If F(x) = 3x^2 - 5x and G(x) = 2x - 4, find G of F(2) and F of G(2) I'm having trouble with this problem. Any help is appreciated. Thanks.      Log On


   

Question 81404: If F(x) = 3x^2 - 5x and G(x) = 2x - 4, find G of F(2) and F of G(2)
I'm having trouble with this problem. Any help is appreciated. Thanks.
Answer by SMM52091(3) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find g(f(2)), just find f(2) and then g() it. For example...
f%28x%29+=+3x%5E2+-+5x
f%282%29+=+3%282%5E2%29+-+5%282%29
f%282%29+=+3%284%29+-+10
f%282%29+=+12+-+10
f%282%29+=+2 Please note that f(2) equaling 2 is just a coincidence.
So the question asks for g(f(2)). Since f(2) equals 2, then g(f(2)) is the same thing as g(2). Now apply the g formula.
g%28x%29+=+2x+-+4
g%282%29+=+2%282%29+-+4
g%282%29+=+4+-+4
g%282%29+=+0
So g(f(2)) = 0.
Now just because g(f(2)) equals 0 doesnt mean f(g(2)) equals 0. You need to redo it for the second problem, just in a different way. Find g(2) and then f() it.
g%28x%29+=+2x+-+4
g%282%29+=+2%282%29+-+4
g%282%29+=+4+-+4
g%282%29+=+0
Since g(2) = 0, then f(g(2)) is the same thing as f(0). So find the function of 0 with the f(x) formula.
f%28x%29+=+3x%5E2+-+5x
f%280%29+=+3%280%5E2%29-+5%280%29
f%280%29+=+3%280%29+-+0
f%280%29+=+0+-+0
f%280%29+=+0
So f(g(2)) = 0
Hope I could help