SOLUTION: Consider the function f(x)=3x-6 and g(x)=x/3+2. A) Find f(g(x)). B) Find g(f(x)). C) Determine whether the functions f and g inverse of each other.

Algebra ->  Functions -> SOLUTION: Consider the function f(x)=3x-6 and g(x)=x/3+2. A) Find f(g(x)). B) Find g(f(x)). C) Determine whether the functions f and g inverse of each other.      Log On


   

Question 685001: Consider the function f(x)=3x-6 and g(x)=x/3+2. A) Find f(g(x)). B) Find g(f(x)). C) Determine whether the functions f and g inverse of each other.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
f(g(x)) = 3%28x%2F3%2B2%29-6
= 3%28x%2F3%29+%2B+3%282%29+-+6
f(g(x))= x
...
...
g(f(x)) = %283x-6%29%2F3+%2B+2
= 3x%2F3+-+6%2F3+%2B+2
g(f(x)) = x
...
...
f(x) = 3x - 6
y = 3x - 6
y + 6 = 3x
x = %28y%2B6%29%2F3
f%5E-1%28x%29+=+x%2F3+%2B+2
so g(x) is an inverse function of f(x)
and
g(x) = x%2F3+%2B+2
y = x%2F3+%2B+2
y - 2 = x%2F3
x = 3(y-2)
g%5E-1%28x%29+=+3x+-+6%29
so f(x) is an inverse function of g(x)
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