find the composite function

Question

Given the  f(x)= 4/x² and g(x) = 3-2x, find the composite function (f º g) and simplify.

Answer 1

Given f(x) and g(x),   (f º g)(x) = f(g(x)) 

 

with f(x) = 4/x²   and g(x) = 3-2x,  First apply g, then apply f to that result as follows:

 

g(x) = 3x-2

 

f(g(x)) =  4/ (3 - 2x)²  = 4/ ((3-2x)(3-2x))

f(g(x)) = 4/ (4x²-12x+9)

          

 

Answer 2

f(x)= 4/x² and g(x) = 3-2x

 

f(g(x)) = 4/ (3 - 2x)²

 

f(g(x)) = 4/(4x² - 12x + 9)