SOLUTION: Can you please help me with the following problem: Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5) I know that the domain of f(x) is (-infinity,2)U (2,infinity) an

Question 193570: Can you please help me with the following problem:
Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5)
I know that the domain of f(x) is (-infinity,2)U (2,infinity) and g(x) is (-infinity,5)U (5,infinity)
I know that f(x) has got to be set to the number that the domain cannot use in g(x)
So that would be 5=4/(x-2)
Then multiply each side by (x-2). (x-2)(5)=(4/(x-2))(x-2) this cancel out the denominator.
Then the problem would be 5x-10=4, subtract 10 from each side to isolate the variable. 5x-10+10=4+10 => 5x=14. Then to isolate x, x would have to be divided by 5. 5x/5=14/5 => x=14/5
So would the domain be (-infinity,2)U(2,(14/5))U((14/5),5)U(5,infinity)?
please let me know if any mistakes were made
thanks!

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the domain of f(g(x)). F(x)= 4/(x-2) and g(x)=3/(x-5)
f[g(x)] = f[3/(x-5)] = 5/[3/(x-5) -2] = 5/[(3-2x+10)/(x-5)]
= 5/[13-2x/(x-5)/
= [5(x-5)]/[13-2x]
-----------------------
Domain: All Real numbers except x = 13/2
==============================================
Cheers,
Stan H.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's find the domain of g(x):

Start with the given function

Set the denominator equal to zero

Add 5 to both sides. So plugging 5 into the denominator results in a division by zero. So we must take this value out of the domain.

So the domain of g(x) is: x can be any real number but

------------------------------------------------------------
Now let's find the domain of f(g(x))

Start with the given function

Plug in

Multiply EVERY term by the inner LCD to clear out the inner fractions.

Distribute

Combine like terms.

Set the denominator equal to zero

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So we must take out of the domain (since this value causes a division by zero)

So the domain of f(g(x)) is: x can be any real number but . In addition, we made a previous statement that

So this means that the domain of f(g(x)) in interval notation is

RELATED QUESTIONS
I really need some help! Can anyone help me? If f(x)=ln x, g(x)=e^4^x, and h(x)= x^3,... (answered by sheldonbbtrocks)
With this problem, I need to find the function and state the domain of each given the... (answered by venugopalramana)
CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM PLEASE: Find the domain of the composite... (answered by gonzo)
Can someone please help me with these problems. I do not even know where to start. please (answered by stanbon)
I kind of understand how to do these f◦g and g◦f problems, but I dont know... (answered by stanbon)
Could you please help me with this problem i dont understand it use f(x)={{{4x^-5}}} (answered by stanbon)
can you help me evaluate the following problem f(x)=2x-5 and g(x)= x^2+3x+4 f(2) -... (answered by reviewermath)
If f(x)=2x^2+3 and g(x)=x-5 find: a. (f o g)(3) b. (g o f)(3) I am unsure as to where... (answered by drcole)
Can you please help me with this problem: Find each value given that f(x)=2x+1... (answered by venugopalramana,rapaljer)