Question

(b) Find f ◦ g and g ◦ f, where f(x) = x
2 + 1 and g(x) = x + 2, are functions from R to
R.
(c) Find f + g and fg for the functions f and g given in part (b).

Answer 1

(b) $(f \circ g)(x) = f(g(x)) = (g(x))^2+ 1 = (x+2)^2+1 =$ $x^2 +4x+4+1= x^2+4x+5$

$(g \circ f)(x) = g(f(x)) = f(x) +2 = x^2+1+2 = x^2+3$

(c) $(f+g)(x) = f(x) + g(x) = x^2+1 +x+2 = x^2+x+3$

$(fg)(x) = f(x) \cdot g(x) = (x^2+1)(x+2) = x^3 + 2x^2+x+2$