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

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .