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consider the function
f(x)=2x+8/x+6, g(x)=6x-8/2-x

a. what is f(g(x))?
b. give any vales of x that need to be excluded f(g(x)).

c. what is g(f(x))?
d. give any values of x that need to be excluded from g(f(x)).

e. Are the function f and g inverse of each other?

  • math -

    f(g) = (2g+8)/(g+6)
    = (2(6x-8)/(2-x)+8)/((6x-8)/(2-x)+6)
    = x

    f(-6) is not defined, but since g(x) is never -6, the domain is all reals.

    g(f) = (6f-8)/(2-f)
    = (6(2x+8)/(x+6)-8)/(2-(2x+8)/(x+6))
    = x

    f and g are inverses since f(g) = g(f) = x

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