Composite Functions: f o g (x) = Abs(x), f(x) = root(x), g(x) = Abs(x)

AI Thread Summary
The discussion revolves around the composite functions f o g (x) = Abs(x), f(x) = root(x), and g(x) = Abs(x). Participants debate whether f(x) should be equal to sqrt(x) or if g(x) should be sqrt(x) instead. Clarifications are made regarding the correct interpretation of the problem, with some suggesting that if f o g (x) = Abs(x), then f(x) could be x^2 and g(x) = sqrt(x). The domain of g is noted as x ≥ 0, leading to the conclusion that x = |x| in this context. The conversation emphasizes the importance of correctly identifying the functions involved in the composite.
Larrytsai
Messages
222
Reaction score
0
f o g (x) = Abs(x)
f(x)=?
g(x)= root(x)

im thinking f(x) is = to root(x) correct me if I am wrong?
 
Physics news on Phys.org
f(x) = sqrt(x) doesn't work. Are you sure you have this problem written correctly? Could it be g o f (x) = Abs(x)? That would make more sense with g(x) being sqrt(x). Of if it is indeed f o g (x) = Abs(x), could it be that f(x) = sqrt(x) and you need to find g(x)?
 
its correct way i took it straight from the book.
 
OK.
If f(x) = x2 and g(x) = \sqrt{x}
then (f~\circ~g )(x) = x.

Since the domain of g = {x | x \geq 0}, then x = |x| in this case.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Finding the domain of a composite function
Replies
10
Views
2K
Solution of inequality of composite function involving inverse
Replies
13
Views
2K
Understanding the graphical effect of f(x+a)
Replies
19
Views
2K
Find the domain and the range of ##f-3g##
Replies
3
Views
2K
How does this composite function simplify to 2(2^x) ?
Replies
3
Views
2K
Prove that ## g(x)=f(x)\log {x}-\int_{2}^{x}t^{-1}f(t)dt ##.
Replies
7
Views
1K
Solve the problem involving the cubic function
Replies
12
Views
2K
##f(x+y) =f(x) f(y)## and ##f(1)+f(2)=5## then find ##f(-1)=?##
Replies
49
Views
3K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
Replies
8
Views
3K
Is ##f(x)=2^{x}-1## considered an exponential function?
Replies
12
Views
2K

Hot Threads

Recent Insights

Back
Top