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

Question

find

(f+g) (x)

(fg) (x)

(g o f) (x)

(f o g) (1)

Answer 1

f(x) = x-1

g(x) = x^2 +1

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

(fg)(x) = f(x)g(x) = (x-1)(x^2+1) = x^3 -x^2 +x -1

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

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