SOLUTION: Please help me with this problem: g(x)=4x-1, g(h(x))=12x, find h(3). How do I figure out h(x)? Thank you.

Algebra ->  Functions -> SOLUTION: Please help me with this problem: g(x)=4x-1, g(h(x))=12x, find h(3). How do I figure out h(x)? Thank you.       Log On


   

Question 14424: Please help me with this problem: g(x)=4x-1, g(h(x))=12x, find h(3). How do I figure out h(x)? Thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this:
g%28x%29+=+4x-1
g%28h%28x%29%29+=+12x
g%28h%28x%29%29+=+4%28h%28x%29%29-1
4%28h%28x%29%29-1+=+12x Solve for h(x)
4%28h%28x%29%29+=+12x%2B1 Divide by 4.
h%28x%29+=+3x+%2B+1%2F4
Check:
g%28h%28x%29%29=+4%283x%2B1%2F4%29-1%29
g%28h%28x%29%29+=+12x+%2B+4%2F4+-+1 = 12x
h%283%29+=+3%283%29+%2B+1%2F4
h%283%29+=+9%2B%281%2F4%29 = 9.25