The document provides solutions to two pairs of functions f(x) and g(x) to determine if they are inverses. For the first pair, f(x) = -6x and g(x) = 1/6x, it is found that f(g(x)) = -1/x and g(f(x)) = -1/36x, so they are not inverses. For the second pair, f(x) = 1/4x and g(x) = 1/4x, it is found that f(g(x)) = g(f(x)) = 1/16x, so these functions are inverses.
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Submit Quiz Question #1 10 For each pair of functions [and g below,.pdf
1. Submit Quiz Question #1 / 10 For each pair of functions [and g below, find f(g(x)) and g(f(x)) .
Then, determine whether land g are inverses of each other. Simplify your answers as much as
possible. (Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
Solution
f(x) = -6x
g(x) = 1/6x
f(g(x)) = -6 *(1/6x)
= -1/x
g(f(x)) = 1/6*(-6x) = -1/ 36x
they are not inverse of each other beacuse f(g(x)) and g(f(x)) are not equal
2)
f(x) = 1/4x
g(x) = 1/4x
f(g(x)) = 1/4*(4x)
= 1/16x
g(f(x)) = 1/4*(4x) = 1/16x
f and g are inverse of each other.. beacuse f(g(x)) and g(f(x)) are equal