Let f(x) = 2x - 3 and g(f(x)) = 5-4x. Find g(4).
g( f(x) ) = 5 - 4x
We want to find g(4) , that is, we want to find g when...
f(x) = 4
Since f(x) = 2x - 3 , we can replace f(x) with 2x - 3 .
2x - 3 = 4
Add 3 to both sides.
2x = 7
Divide both sides by 2 .
x = 7/2
Now we know that when x = 7/2 , f(x) = 4 .
g( f(x) ) = 5 - 4x
Replace every instance of x with 7/2 .
g( (f(7/2) ) = 5 - 4(7/2)
Since f(7/2) = 4 , we can say...
g(4) = 5 - 4(7/2)
g(4) = -9