SOLUTION: find the composition function Let f(x) = log(x^2-5) and let g(x) = x+6. Find the composite finctions, f[g(x)] and g[f(x)]

Algebra ->  Sequences-and-series -> SOLUTION: find the composition function Let f(x) = log(x^2-5) and let g(x) = x+6. Find the composite finctions, f[g(x)] and g[f(x)]      Log On


   

Question 106082: find the composition function
Let f(x) = log(x^2-5) and let g(x) = x+6. Find the composite finctions, f[g(x)] and g[f(x)]
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=log%28%28x%5E2-5%29%29
g%28x%29=x%2B6
f%28g%28x%29%29=log%28%28x%2B6%29%5E2-5%29Substitute.
f%28g%28x%29%29=log%28%28x%5E2%2B12x%2B36%29-5%29 Use the FOIL (First Outer Inner Last) Method.
f%28g%28x%29%29=log%28%28x%5E2%2B12x%2B31%29%29Simplify.
g%28f%28x%29%29=%28log%28%28x%5E2-5%29%29%29%2B6Substitute.
g%28f%28x%29%29=%28log%28%28x%5E2-5%29%29%29%2Blog%28%2810%5E6%29%29Use your logarithm rules.
g%28f%28x%29%29=log%28%2810%5E6%2A%28x%5E2-5%29%29%29%29SImplify.