what is (f*g)(x) if f(x)=3x+6 and g(x)=1/3x-2?
To find the result of the function (f*g)(x), we need to substitute the expression for g(x) within the expression for f(x).
First, let's write out the given functions:
f(x) = 3x + 6
g(x) = (1/3)x - 2
To find (f*g)(x), we substitute g(x) into f(x) by replacing x in f(x) with the expression for g(x):
(f*g)(x) = f[g(x)]
Replace x in f(x) with the expression for g(x):
f[g(x)] = f[(1/3)x - 2]
Now, substitute the expression (1/3)x - 2 into f(x):
f[(1/3)x - 2] = 3((1/3)x - 2) + 6
Simplify the equation:
3((1/3)x - 2) + 6 = x - 6 + 6 = x
Therefore, the result of the function (f*g)(x) is x.