Question

Consider the functions f(x)=-x-3 an g(x)=- 1/2(x+3). Find the f(g(x)), find the g(f(x)) and determine whether the function f and g are inverse of each other.

Answer 1

Substituting the given expressions:
f(g(x)) = f(-1/2(x+3)) = (-(-1/2(x+3)) -3 = 1/2x -3/2
We know already the functions are not inverse of each other since the result is not x.

g(f(x)) = -1/2((-x-3)+3) = -1/2(-x) = 1/2x
This, too, is not "x", so we know f(x) and g(x) are not inverses.

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Consider the graphs of the two functions. They are not symmetrical about the line y=x, so cannot be inverse functions.