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f(x) and g(x) are inverses

Step-by-step explanation:

* Lets check the inverse function

- If f(x) = y has a domain = x and a range = y, then f^-1 is the

  inverse of f with a domain  = y and a range = x

- f(x) = f^-1(x) = x

* Now lets solve the problem

∵ f(x) = 8/x

∵ g(x) = 8/x

∴ fg(x) = f(8/x)

∴ fg(x) = 8/(8/x) = 8 ÷ 8/x ⇒ change division sign to the multiplication

  sign and reciprocal the fraction after the division sign

∴ fg(x) = 8 × x/8 = x

* Now lets find gf(x)

∴ gf(x) = g(8/x)

∴ gf(x) = 8/(8/x) = 8 ÷ 8/x

∴ gf(x) = 8 × x/8 = x

∵ f(x) = f^-1(x) = x

* fg(x) = gf(x) = x

∴ f(x) and g(x) are inverses

what do you need me to answer?

step-by-step explanation: