SOLUTION: If f(x)=5/x and g(x)=2/2x+1 , find the functions (a,b) and their domains. a.) (f o g)(x) I did 5/1/2/2x+1 and I multiplied 2 and 1 and multiplied 5 and 2x+1 to get 10x+5/2 . I t

Question 1052272: If f(x)=5/x and g(x)=2/2x+1 , find the functions (a,b) and their domains.
a.) (f o g)(x) I did 5/1/2/2x+1 and I multiplied 2 and 1 and multiplied 5 and 2x+1 to get 10x+5/2 . I then factored out the 5 in the numerator to get 5(2x+1) (Not positive if I need to factor the numerator or not) and then the denominator stayed at 2. I think the correct answer to this is 5(2x+1)/2 . And the Domain= (-infinity, 1/2)u(1/2, +infinity). (Not sure if this Domain is correct, nor am I sure how I got it).

b.) (g o f)(x) I am not sure how to solve this one. I am stuck at 2/2(5/x)+1. I am not sure how to get the fraction out of the denominator.
Anything helps, thank you.
-Garrett
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Part A

Replace EVERY copy of x with g(x)

Focus only on the right side. Replace g(x) with it's equivalent expression. Now simplify

Since (f o g)(x) is the same as f(g(x)), this means that (f o g)(x) is equal to

The simplified form of the equation above leads to no domain issues. However, if you consider the original function before you simplify, then leads to a division by zero error.
So we must kick that out of the domain.

So the domain of (f o g)(x) is (-infinity, -1/2) U (-1/2, infinity). Any other number works in the domain.

====================================================================

Part B

Replace EVERY copy of x with f(x)

Plug in f(x) = 5/x. Simplify.

So (g o f)(x) is equivalent to

Here we can't have x equal 0 or -10. Those values make the denominator zero. Any other value will work.

So the domain of (g o f)(x) is (-infinity, -10) U (-10, 0) U (0, infinity)
RELATED QUESTIONS
given the functions f(x) = 1-3x^2 and g(x) = sqrtx-1, find the functions (f+g) , (f-g),... (answered by josgarithmetic)

15. If f(x) =2x2+1 and g(x)=x-3, find (f o g)(x). a. (f o g)(x) = 2x 2 - 17 b. (f o... (answered by Fombitz)

for the indicated functions f and g, ﬁnd the functions f + g, f - g, fg, and f|g, (answered by ewatrrr)

Let f(x)=-2x -1 and g(x)=x^2+3 Find (f o g)... (answered by Fombitz)

2. For the functions f(x) = - x + 1, g(x) = 4x �4 a. Find the composite... (answered by lwsshak3)

3. If f(x)=square root 2x^2-1 and g(x)=x^1/2, find (and simplify) a) (f+g)(x) b)... (answered by CPhill)

I need to find the functions (f o g), (g o f),(f o f), and (g o g) and their domains for: (answered by mukhopadhyay)

for the indicated functions f and g, ﬁnd the functions f + g, f - g, fg, and f|g, (answered by ewatrrr)

If f(x)= square root 2x^2-1 and g(x)=x^1/2, find and simplify a) (f+g)(x) b) (f-g)(x) (answered by Alan3354)