SOLUTION: F(x)=10x G(x)=x+3 Find 1. F(g)(x) 2. The inverse of f(g) 3. The inverse of g(f)

Question 1141925: F(x)=10x
G(x)=x+3

Find 1. F(g)(x)
2. The inverse of f(g)
3. The inverse of g(f)

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Don't mix cases. In a single problem, F(x) and f(x) could be very different functions.

1. f(g(x)) = f(x+3) = 10(x+3)

2. inverse of f(g)

g adds 3 to the input; f multiplies the input by 10.
So f(g(x)) adds 3 to the input and then multiplies it by 10.
The inverse does the opposite operations in the opposite order: divide by 10 and subtract 3.

ANSWER: inverse of f(g(x)) = (x/10)-3

3. inverse of g(f)

(similar explanation...)

ANSWER: inverse of g(f(x)) = (x-3)/10

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