Question 1148429
these look like inverses of each other because f(g(x)) = x and g(f(x)) = x.


here's a reference.


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you have f(x) = x^2-2.
the domain is [0,infinity)
the range is [-2,infinity)


you have g(x) = sqrt(x+2)
the domain is [-2,infinity)
the range is [0,infinity)


here's the graph of f(x) = x^2-2


<img src = "http://theo.x10hosting.com/2019/110801.jpg" alt="$$$" >


here's the graph of g(x) = sqrt(x+2)


<img src = "http://theo.x10hosting.com/2019/110802.jpg" alt="$$$" >


you solve for f(g(x)) as follows:


f(x) = x^2-2
g(x) = sqrt(x+2)
to get f(g(x)), you replace the x in f(x) with g(x).
this means you relace the x in f(x) with sqrt(x+2).
f(g(x)) = (sqrt(x+2))^2-2 = x+2-2 = x


g(x) = sqrt(x+2)
f(x) = x^2-2
to get g(f(x)), you replace the x in g(x) with f(x).
this means you replace the x in g(x) with x^2-2.
g(f(x)) = sqrt(x^2-2+2) = sqrt(x^2) = x


since f(g(x)) = x and g(f(x)) = x, then the two functions are inverse functions to each other.