Given that
f:x -->3-x
g:x --> x+2/x-5
derive the expression for gf(x)
To derive the expression for gf(x), we need to substitute f(x) into g(x).
First, let's find f(g(x)):
f(g(x)) means we need to substitute g(x) into f(x).
Step 1: Replace x in f(x) with g(x):
f(g(x)) = 3 - g(x)
Step 2: Replace g(x) with the expression for g(x):
f(g(x)) = 3 - [x+2 / x-5]
Now, simplify the expression inside the brackets:
f(g(x)) = 3 - [(x+2)/(x-5)]
To make the expression easier to read, you can also write it as:
f(g(x)) = 3 - (x+2) / (x-5)
That's the derived expression for gf(x).