# Thread: 2 discrete math prob

1. ## 2 discrete math prob

i have two problems that i need help with real quick if someone could please help me...

the first is..

1. Let A=B=C=R, and let f:A-->B, g:B-->C be define by f(a)=a^2-3a+5 and g(b)=2b+4. Find:

a) (f o g)(3)
b) (g o f)(x)

the second problem is:

2. f(x)=4x-8. Find f^-1.

Thanks for anyone that can help!!!!

~Rich

2. Originally Posted by mathnoobie25
i have two problems that i need help with real quick if someone could please help me...

the first is..

1. Let A=B=C=R, and let f:A-->B, g:B-->C be define by f(a)=a^2-3a+5 and g(b)=2b+4. Find:

a) (f o g)(3)
b) (g o f)(x)
Ok, so for a) we have
(f o g)(3) = f(g(3)) (function composition)
= f(2*3 + 4) (by defn of g)
= f(10) (simplifying)
= 10^2 - 3*10 + 5 (by defn of f now)
= 75.

I'm sure you can do b) now - it's the same thing, just this time you won't end up with a number, you'll end up with something involving x's.

Originally Posted by mathnoobie25
the second problem is:

2. f(x)=4x-8. Find f^-1.

Thanks for anyone that can help!!!!

~Rich
Swap the f(x)'s and x's, like so:

x = 4*f(x) - 8.

Now we just solve for f(x) again, ie,

f(x) = (x + 8)/4.

You can check it's the inverse by evaluating f(f^-1(a)) and f^-1(f(a)). In both cases we want to end up with just a.

Hope that helps.