1. ## function

Given two functions , f(x)=x^2+3 , where x is real , g(x)=|x|-5 , x is real , find gf(x).

i found gf(x)=x^2-2

is it true that the range of gf(x) is the same as the range of g(x) ? If so,

the range of g(x) is [-5 , infinity) and the range of gf(x) is [-2 , infinity)

why arent they the same ?

2. $\displaystyle g(f(x))=\left | x^2+3 \right |-5$

3. Originally Posted by thereddevils
Given two functions , f(x)=x^2+3 , where x is real , g(x)=|x|-5 , x is real , find gf(x).

i found gf(x)=x^2-2

is it true that the range of gf(x) is the same as the range of g(x) ? If so,

the range of g(x) is [-5 , infinity) and the range of gf(x) is [-2 , infinity)

why arent they the same ?
It is NOT true in general that the range of g(f(x)) is equal to the range of g(x) so your results are hardly surprising.

Originally Posted by Stroodle
$\displaystyle g(f(x))=\left | x^2+3 \right |-5$
Irrelevant since |x^2 + 3| = x^2 + 3 because x^2 + 3 is always positive.

4. Originally Posted by Stroodle
$\displaystyle g(f(x))=\left | x^2+3 \right |-5$
hello strodle , thanks for replying but thats not my question . I would like to know whether the range of g(x) the same as the range of gf(x) ? If i draw the set diagrams with the arrows , i found them to be the same . Take a look at the diagram i attached . gf(x) and g(x) both arrive at the same set

Anyways , gf(x) could be further simplified knowing that x^2+3 is positive .

5. Oh yeah, sorry. I misunderstood the question...