How do you verify if $f (x) = x + 4; g (x) = x - 4$ $f(x)=x+4; g(x)=x-4$ are inverse functions?

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Answer 1 · 2017-06-28T16:12:31

$f \circ g = Id = g \circ f$ $f circ g = text{Id} = g circ f$

$f (g (x)) = g (x) + 4 = x - 4 + 4 = x$ $f(g(x)) = g(x) + 4 = x - 4 + 4 = x$

$g (f (x)) = f (x) - 4 = x + 4 - 4 = x$ $g(f(x)) = f(x) - 4 = x + 4 - 4 = x$

$h (x) = x \Rightarrow h =$ $h(x) = x => h =$ Id

How do you verify if f(x)=x+4; g(x)=x-4f(x)=x+4;g(x)=x−4f(x)=x+4; g(x)=x-4 are inverse functions?