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For each pair of functions f and g below, find f(g(x)) and g(f(x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain ofthe composition.
You do not have to indicate the domain.)

For Each Pair Of Functions F And G Below Find Fgx And Gfx Then Determine Whether F And G Are Inverses Of Each Other Simplify Your Answers As Much As Possible As class=

Sagot :

Answer:

a)  f(g(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

    g(f(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

    f and g are inverses

b)   f(g(x)) = x + 3 + 3 = x + 6

     g(f(x)) = x + 3 + 3 = x + 6

     f and g are not inverses

Step-by-step explanation:

a)

f(g(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

g(f(x)) = [tex]\frac{1}{2(\frac{1}{2x} )}[/tex] = [tex]\frac{1}{\frac{1}{x} } }[/tex] = x

Since f(g(x)) = g(f(x)) = x, then f and g are inverses

b)

f(g(x)) = x + 3 + 3 = x + 6

g(f(x)) = x + 3 + 3 = x + 6

Since f(g(x)) = g(f(x)) ≠ x, then f and g are not inverses

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