How do you prove that f(x) and g(x) are inverses of each other?

Question

#f(x)=(x+3)/2#

#g(x)=2x-3#

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Answer 1 · 2016-12-20T02:49:04

If functions #f(x)# and #g(x)# are inverses, their compositions will equal #x#.

Composition 1: #f(g(x))#

#f(g(x)) = ((2x - 3) + 3)/2 = (2x)/2 = x" "color(green)(√)#

Composition 2: #g(f(x))#

#g(f(x)) = 2((x + 3)/2) - 3 = x + 3 - 3 = x" "color(green)(√)#

Hopefully this helps!