How do you solve this math problem involving composition of functions?

Question

If f(g(x))= 2x-1 and g(x)= 2x+3 find f(x). 
Okay so if I plug g(x)= 2x+3 into the unknown f(x) then I have
f(2x+3)= 2x-1. So at this point what do I do next? Am I suppose to isolate f? If I subtract 3 from both sides I have f(2x)= 2x-4. If I subtract 2x from both sides then I have f( )= - 4. 
But the answer is f(x) = x- 4. Can someone please help me. I am so close to solving this.

? · Accepted Answer

call g(x)=y so y=2x+3
now solve for x:
x = (y-3)/2

Now substitute in for f(g(x))
f(g(x))= 2*((y-3)/2) -1
=(y-3) - 1
=y-4  but recall y = g(x) so
f(g(x)) = g(x) -4

Now substitute x in for g(x) on both sides to get
f(x) = x-4

bskelkar · Answer

Let 2x+3 = t so x = (t-3)/2.
Now f(t) = 2x-1 = t-3-1=t-4.So f(x) = x-4. Simple!

How do you solve this math problem involving composition of functions?

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