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?

2 is not in the domain of f of g

Step-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