SOLUTION: Using the functions f(x) = x + 4 and g(x) = 2x - 5, find the following. ({{{g^-1}}}◦{{{f^-1)}}}(x) ({{{f^-1}}}◦{{{g^-1)}}}(x) (f◦g)^-1 (x) (g◦f)^-1(x)

Question 1050585: Using the functions f(x) = x + 4 and g(x) = 2x - 5, find the following.
(◦(x)
(◦(x)
(f◦g)^-1 (x)
(g◦f)^-1(x)
To attempt the problem so far what I did was first find the inverse of f(x) & g(x). The inverse I got for f(x) = x-4 & g(x) = (1/2)x+(5/2)
I am not sure how to attempt the rest of the problem from here though.
For example, for #1 do I do g^-1(f^-1(x))?
I would appreciate if anyone could give me a detailed response on how to work the problems.
Answer by josgarithmetic(39626) (Show Source): You can put this solution on YOUR website!
Clarify your problem description and question. I could guess what you are given and asked, but I want to clearly know what you are trying to solve.

Are you asking for the composition of inverse functions?
Are you asking for the multiplication of two inverse functions?

Show unmistakable symbolism for what you are asking.
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SOLUTION: Using the functions f(x) = x + 4 and g(x) = 2x - 5, find the following. ({{{g^-1}}}&#9702;{{{f^-1)}}}(x) ({{{f^-1}}}&#9702;{{{g^-1)}}}(x) (f&#9702;g)^-1 (x) (g&#9702;f)^-1(x)

SOLUTION: Using the functions f(x) = x + 4 and g(x) = 2x - 5, find the following. ({{{g^-1}}}◦{{{f^-1)}}}(x) ({{{f^-1}}}◦{{{g^-1)}}}(x) (f◦g)^-1 (x) (g◦f)^-1(x)