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!
Thanks in advance.
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