Let f(x) = x2 + x - 1 and g(x) = x - 1, then determine f(g(x)) - g(f(x))

Question

I would like this one done for me, please as I don"t have an example like this.

Answer 1

f(x) = x^2 + x - 1;  g(x) = x - 1;  

 

f(g(x)) - g(f(x) = f(g) - g(f) = (g^2 + g - 1) - (f - 1)

 

 = [(x - 1)^2 + (x - 1) - 1] - [(x^2 +x - 1) - 1]

 

 = [(x^2 - 2x + 1) + x - 2] - [x^2 + x - 2]

 

 = [x^2 - x - 1] - [x^2 + x - 2]

 

 = -2x + 1