The calculator will find the compositions (f∘g)(x), (g∘f)(x), (f∘f)(x), and (f∘g)(x) of the functions f(x) and g(x), with steps shown. It will also evaluate the compositions at the specified point if needed.
Related calculator:
Operations on Functions Calculator
Solution
(f∘g)(x)=f(g(x))=f(x+7)=(x+7)2+(x+7)1=(x+7)(x+8)1
(g∘f)(x)=g(f(x))=g(x2+x1)=(x2+x1)+7=7+x2+x1
(f∘f)(x)=f(f(x))=f(x2+x1)=(x2+x1)2+(x2+x1)1=x2+x+1x2(x+1)2
(g∘g)(x)=g(g(x))=g(x+7)=(x+7)+7=x+14
Answer
(f∘g)(x)=(x+7)(x+8)1A
(g∘f)(x)=7+x2+x1A
(f∘f)(x)=x2+x+1x2(x+1)2A
(g∘g)(x)=x+14A