Question

If f(x)=x-1/3 and g(x)=3x+1, what is (f*g)(x) 3x+1 x-3

Answer 1

The correct answer is:  [D]:  " x " .
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Explanation:
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f (g(x))  =  f(3x + 1) = (3x + 1 - 1)  / 3  =  (3x / 3)  = x  .

The answer is:  " x " .

→  which is:  "Answer choice:  [D]:  " x " .
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Answer 2

This is a composite.  Another way to write them is f(g(x)).  Take the function g(x) and stick it in for x in f(x).  Like this: $f(g(x))= \frac{(3x+1)-1}{3}$.  But we aren't done cuz there's some simplifying there to do.  $f(g(x))= \frac{3x}{3}$ and canceling out the 3's we get just a simple x as our answer.  The choice is the last one above as your answer.