F(x)=1/x-2 , g(x)=2x+1/x
a. use composition to prove whether or not the functions are inverses of each other.
b. express the domain of the compositions using interval notation.

A. They are inverses of each other.

Step-by-step explanation:

A.

If they are inverses of each other then f(g(x)) will be = x.

f(g(x)) =   1 /  ( (2x + 1)/ x) - 2)

= 1 / ( 2x + 1 - 2x)/ x

= 1 /  1/x

= x.

So they ARE inverses of each other.

Yes, they are inverse of each other.

Domain =

Step-by-step explanation:

We  re given the following:

If we calculate the composite function, it will be of the form:

Since, f(g(x)) = g(f((x)) = x, the functions are inverse of each other.

The domain of composite functions, f(g(x)) and g(f((x)) are the values that x can take, so the domain for composite number is all real numbers that is

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."