Given-the-function-f-x-x-1-3x-and-g-x-x-1-Find-a-fg-b-f-g-c-gf-1-x-

Question Number 32640 by Rio Mike last updated on 30/Mar/18

G i v e n t h e f u n c t i o n f : x \to \frac{x + 1}{3 x}

a n d g : x \to x - 1 . Find

a) fg

b) f ° g

c) {g f}^{- 1} (x)

Answered by Joel578 last updated on 30/Mar/18

f (x) = \frac{x + 1}{3 x}, g (x) = x - 1

(f \circ g) (x) = f (x - 1) = \frac{(x - 1) + 1}{3 (x - 1)} = \frac{x}{3 x - 3}

(g \circ f) (x) = g (\frac{x + 1}{3 x}) = \frac{x + 1}{3 x} - \frac{3 x}{3 x} = \frac{1 - 2 x}{3 x}

f^{- 1} (x) = \frac{1}{3 x - 1}

(g \circ f^{- 1}) (x) = g (\frac{1}{3 x - 1}) = \frac{1}{3 x - 1} - \frac{3 x - 1}{3 x - 1} = \frac{2 - 3 x}{3 x - 1}

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