SOLUTION: Given the functions f(x) = x + 2 and g(x) = 3^x , Determine all values of x for which f(g(x)) = g(f(x)).

Algebra ->  Functions -> SOLUTION: Given the functions f(x) = x + 2 and g(x) = 3^x , Determine all values of x for which f(g(x)) = g(f(x)).       Log On


   

Question 1162439: Given the functions f(x) = x + 2 and g(x) = 3^x , Determine all values of x for which f(g(x)) = g(f(x)).
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


f%28g%28x%29%29+=+3%5Ex%2B2
g%28f%28x%29%29+=+3%5E%28x%2B2%29

3%5Ex%2B2+=+3%5E%28x%2B2%29
3%5Ex%2B2+=+%283%5Ex%29%283%5E2%29+=+9%2A3%5Ex
2+=+8%2A3%5Ex
3%5Ex+=+0.25
xlog%28%283%29%29+=+log%28%280.25%29%29
x+=+log%28%280.25%29%29%2Flog%28%283%29%29
x = -1.26186 to 5 decimal places

A graph; f(g(x)) red, g(f(x)) green...

graph%28400%2C400%2C-3%2C1%2C-1%2C5%2C3%5Ex%2B2%2C3%5E%28x%2B2%29%29