Post by: tolga on February 25, 2010, 04:53:21 pm
I can find the domain and range for each but have trouble identifying whether it is defined when comparing the domain and range and what Q2 is tryning to say.
Q1) f(x)=root(x-2) , g(x)=1/x+1 +2 , determine whether f(g(x)) exists and g(f(x)) exists and if so, find the composition functions.
Q2 f(x)=3-root(x) and g(x)= x^2 -1, show that f(g(x)) is not defined. by restricting the domain of g, find a function h such that f(h(x)) is defined.
Q3 f(x)=1/(x+a)^2 and g(x)=root(x), determine values of a such that f(g(x)) exists.
Post by: the.watchman on February 25, 2010, 04:57:22 pm
The range can be determined from the domain.
Basically, for Q2, because
In this case, Dom f =
Post by: tolga on February 25, 2010, 05:12:20 pm
Post by: the.watchman on February 25, 2010, 05:17:57 pm
sorry but i dont understand anything you are sayin
Erm...sorry! I'll try again...
To find the domain of a composite function, you work out the domain of the function inside f(x), in this case it is g(x). The domain of the composite is equal to this.
To do Q2, you need to make f(g(x)) defined, so you will need to restrict the domain of g(x)
Now considering that, for a composite function (such as f[g(x)] ) to be defined, the range of g must be within the domain of f.
In this case, it is not, because [-1,infinity) is not within [0,infinity)
Therefore, you need to find the instance when the range of g is within [0,infinity)
If you visualise the graph of g, you will find that for the range of g to be within [0,infinity), the domain of g must be either (-infinity,-1] or [1,infinity)
Using this restricted domain, you can find f(h(x)) and it will be defined.
Hope this is better :)