If f(x)=4x+3 and g(x)= the square root of x-9, which is true? 2 is in the domain of f of g or 2 is not in the domain of f of g?

Accepted Solution

Answer:2 is not in the domain of f of gStep-by-step explanation:* Lets revise at first the meaning of f of g (composite function)- A composite function is a function that depends on another function- A composite function is created when one function is substituted into  another function - Example:# f(g(x)) is the composite function that is formed when g(x) is   substituted for x in f(x).- In the composition (f ο g)(x), the domain of f becomes g(x)* Now lets solve the problem∵ f(x) = 4x + 3∵ g(x) = √(x - 9)- Lets find f(g(x)), by replacing x in f by g(x)∴ f(g(x)) = f(√(x - 9)) = 4[√(x - 9)] + 3∴ f(g(x)) = 4√(x - 9) + 3∵ The domain of f is g(x)- The domain of the function is the values of x which make the   function defined∵ There is no square root for negative values∴ x - 9 must be greater than or equal zero∵ x - 9 ≥ 0 ⇒ add 9 for both sides∴ x ≥ 9∴ The domain of f of g is all the real numbers greater than or equal 9∴ The domain = {x I x ≥ 9}∵ 2 is smaller than 9∴ 2 is not in the domain of f of g