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f(x)=1+x/1-x , g(x) = x/1-x find fog and gof and state the domain of the composition.

f(x) = (1+x)/(1-x), g(x) = x/(1-x)

fog = f(g(x)) = (1 + g)/(1 – g)

fog = (1 + x/(1 – x)) / (1 – x/(1 – x))

fog = {(1 – x + x)/(1 – x)} / {(1 – x – x)/(1 – x)}

fog = {(1 – x + x)} / {(1 – x – x)}

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

Domain is (-ꝏ, ½) U (1/2, ꝏ)

gof = g(f(x)) = f/(1 – f)

gof = {(1 + x)/(1 – x)} / {1 – (1 + x)/(1 – x)}

gof = {(1 + x)/(1 – x)} / {[1 – x –  (1 + x)]/(1 – x)}

gof = {(1 + x)} / {[1 – x –  (1 + x)]}

gof = {(1 + x)} / {-2x}

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

Domain is (-ꝏ, 0) U (0, ꝏ)

by Level 11 User (81.5k points)

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