indicated composite #1

Question

find the indicated composite for the pair of functions

 

 f(x)=6x+12;  g(x)=4x-1

    Find(f*g)(x)

Answer 1

Hi Carlos,

 

I'm going to give a different answer from that provided by Deanna, as I was taught this a little differently. For reference, you can see

 

  http://en.wikipedia.org/wiki/Function_composition

 

I was taught that (f * g)(x) = f(g(x)) -- that is, we have an input x; apply function g to x; then take that result as input and apply function f. So for our f and g:

 

1) We apply function g to x and have (4x-1)

 

2) We apply function f to an input of (4x-1) and have 6*(4x-1) + 12

 

I leave it to you to simplify the answer of 6*(4x-1) + 12 -- I think you will find it to be somewhat different from the first answer we have.

 

Hope this helps you.

Answer 2

Carlos,

 

The composite function is (6x+12)(4x-1) or 24x^2+42x-12. (Use the FOIL method - first, outer, inner last).

 

Hope that helps,

Deanna