Question

Let lower f left-parenthesis x right-parenthesis equals Start Root x minus 2 End Root and lower g left-parenthesis x right-parenthesis equals Start Root x plus 7 End Root. Find left-parenthesis f dot g right-parenthesis left-parenthesis x right-parenthesis. Assume all appropriate restrictions to the domain.
(1 point)
Responses

left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals x squared plus 5 x minus 14
Image with alt text: left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals x squared plus 5 x minus 14

left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals x squared plus 9 x minus 14
Image with alt text: left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals x squared plus 9 x minus 14

left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Root x squared plus 9 x minus 14 End Root
Image with alt text: left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Root x squared plus 9 x minus 14 End Root

left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Root x squared plus 5 x minus 14 End Root
Image with alt text: left-parenthesis lower f dot lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Root x squared plus 5 x minus 14 End Root

Answer 1

To find the composition of f and g, we substitute the function g(x) into the function f(x).

f(g(x)) = f(√(x+7)) = √(x+7) - 2

Therefore, the correct response is:

(f∘g)(x) = √(x+7) - 2