Consider the functions
posted by Kayleigh .
Consider the functions
f(x)= 5x+4/x+3(This is a fraction) and
g(x)= 3x4/5x(This is a fraction)
a)Find f(g(x))
b)Find g(f(x))
c)Determine whether the functions f and g are inverses of each other.

Consider the functions 
Steve
f(g) = (5g+4)/(g+3)
= (5(3x4)/(5x)+4) / ((3x4)/(5x)+3)
= x
g(f) = (3f4)/(5f)
= (3((5x+4)/(x+3))4) / (5((5x+4)/(x+3)))
= x
since f(g) = g(f) = x, they are inverses 
Consider the functions 
Kayleigh
What are the values that need to be excluded?

Consider the functions 
Steve
whatever makes the denominator zero must be excluded, since division by zero is undefined.
So, for f(g), x=5 is not allowed, since g(5) is not defined. In addition, since f(3) is not defined, any x where g(x) = 3 must also be excluded. Luckily, there is no such x.
Use similar reasoning for g(f). 
Consider the functions 
Kayleigh
So there are no values to be excluded?

Consider the functions 
Steve
Read what I said. You have to exclude x=5 because g(5) is not defined. Therefore, f(g(5)) is also not defined.
Respond to this Question
Similar Questions

Calculus
We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic … 
AlgebraFunctions
Could you please check my answers and help me with two problems? 
mathplease I really need help!!!!!
Consider the functions f(x)=2x+8/x+6; g(x)=6x8/2x Find f(g(x)) Find g(f(x)) Deterrmine if f and g are inverses of each other. a. What is f(g(x))? 
math
consider the functions f(x)=x^32 and g(x)=3 sqrt x+2: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverse of each other. I have no clue where to even begin! 
math
for the given functions f and g, find the specified value of the following functions and state the domain of each one. f(x)=2+3/x; g(x)=3/x a.(fg)(2)= b.(f/g)(3)= how do I do this? 
pre calculus
consider the functions f(x)=x^33 and g(x)=3 sqrt x+3: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverses of each other. I really need help with these, I don't get it at all. 
College Algebra! help!
Consider the following functions f(x)= (7x+8)/(x+3) and g(x)= (3x8)/(7x) (a) Find g(g(x)) (b) Find g(f(x)) (c) Determine whether the functions f and g are inverses of each other. 
Algebra 2
for the functions f(x) = 5x +50 and g(x) = 1/5x 10 evaluate both f(g(x)) and g(f(x)). Are these functions inverses? 
Math
If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function? 
math
consider the functions f(x)=2x8 and g(x)=x/2+4 (a) Find f(g(x)). (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other (a) What is f(g(x))?