Which of the following are inverse functions: f(x) = 2x - 3 g (x) = (x + 3) / 2 h(x) = 3x + 2

Expert Answers

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We have the functions:

f(x) = 2x - 3

g (x) = (x + 3) / 2

h(x) = 3x + 2

A function f(x) is an inverse of g(x) if f(g(x)) = x.

We test the three functions:

f(g(x)) = f((x + 3)/2) = 2*(x+3)/2 - 3 = x + 3 - 3 = x

This indicates that f(x) and g(x) are inverse functions.

f(h(x)) = f(3x +2) = 2*(3x + 2) - 3 = 6x + 4 - 3 = 6x + 1

This gives that f(x) and h(x) are not inverse functions.

g(h(x)) = g(3x +2) = (3x + 2)/2 = (3/2)x + 1

Again g(x) and h(x) are not inverse functions.

Only the functions f(x) and g(x) are inverse functions.

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