Question

For each pair of functions, find f(g(x)) and g(f(x)).

1. f(x) = x-3/2, g(x) = 2x-3

2. f(x) = x+5/2, g(x) = x^2

Answer 1

1. f(x) = x-3/2, g(x) = 2x-3
f(g(x)) = g(x)-3/2
f(g(x)) = 2x-3-3/2

does that help?

Answer 2

Yes and this is what I did for the first problem:

= f(2x-3)
= (2x-3) -3
= -6x+9/2

Can I leave the answer to be -6x+9/2?

Answer 3

I'm stuck on the first problem with
= g(x-3/2)
= 2(x-3/2) -3

Answer 4

how did you get -6x?

Answer 5

Oh wait I distributed -3 and I see that you can only subtract it... My bad. So would it be like this then:

= f(2x-3)
= (2x-3) - 3/2
= 2x-6/2
= 2x - 3 ?

Answer 6

= f(2x-3)
= (2x-3) - 3/2
= 2x-3 - 3/2 .................. (3=3/1=6/2)
= 2x-6/2 - 3/2
= 2x - 9/2

now try g(f(x))

Answer 7

= g(x-3/2)
= 2(x-3/2)-3
= (x-3)-3
= x-6

Answer 8

= g(x-3/2)
= 2(x-3/2)-3
= (x-3)-3 ← why didn't you distribute the 2 to the x?
= x-6

Answer 9

I missed that one -__- . Gah I'm so bad at math. So:
= g(x-3/2)
= 2(x-3/2)-3
= (2x-6) - 3
= 2x-9