Question

Find f ◦ g and g ◦ f, where f(x) = x
2 + 1 and g(x) = x + 2, are functions from R to
R

Answer 1

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

$$=x^2+4x+4+1$$

$$=x^2+4x+5$$

Answer: x^2+4x+5

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

$$=x^2+3$$

Answer: x^2+3