1. ## Composite Functions

Hello all, i need some help with domain and ranges of composite functions.

1.) f: R --> R, f(x) = X^2 - 4
g: R+ union {0} ----> R, g(x) = sqrt(x)

The question was to find f(g(x)) which i found to be x-4. The other part of the question was to find the range which i was completely lost on. Please HELP!

2. Originally Posted by andrew2322
Hello all, i need some help with domain and ranges of composite functions.

1.) f: R --> R, f(x) = X^2 - 4
g: R+ union {0} ----> R, g(x) = sqrt(x)

The question was to find f(g(x)) which i found to be x-4. The other part of the question was to find the range which i was completely lost on. Please HELP!

See the composite you calculated was by this way
$

{(\sqrt{x})}^2 - 4
$

Since the values of x you can use(ie; its domain) is from 0 to infinity

therfore for those values of x ,the value of your value of function is range

ie;
[-4, +infinity}

3. ## hello

hey, i'm not the brightest spark and i have no idea what you mean. Could you be kind enough to explain it one more time?

4. Originally Posted by andrew2322
hey, i'm not the brightest spark and i have no idea what you mean. Could you be kind enough to explain it one more time?

I am sorry for bad explanation

-See when you found the value of f(g(x)) function what you did was to insert G(x) in place of x

- So when you did that you must have done this in your mind

which you further simplified as
x-4

- Now what I say is that all values of x which can be put in g(x) are now the domain of f(g(x))

-Thus only those values of x which are greater than zero can be included
and thus the domain of f(g(x)) is same as g(x)

-Now when it comes to the function
y=x-4
it can take all the values from -R to +R and y increases as x increases

- BUT since we have restricted the values of x we will not get all the values

-So lets put the lowest value of x (zero) to get the minimum
=0-4 = -4

- The maximum value of x is infinity and so should be the upper value