Question

Determine if the following functions are inverses of each other:
f(x) = 7x + 14
g(x) = (1/7) x - 2

Answer 1

Using composite functions, it is found that since f(g(x)) = g(f(x)) = x, the functions are inverse.

How to verify if two functions are inverse of each other?

This can be verified using composite functions. The functions f(x) and g(x) will be inverse if their composite is of x, that is:

f(g(x)) = g(f(x)) = x.

For this problem, the functions are given by:

• f(x) = 7x + 14.

• g(x) = x/7 - 2.

The compositions are:

• f(g(x)) = f(x/7 - 2) = 7(x/7 - 2) + 14 = x - 14 + 14 = x.

• g(f(x)) = g(7x + 14) = (7x + 14)/7 - 2 = x + 2 - 2 = x.

Since f(g(x)) = g(f(x)) = x, the functions are inverse.

More can be learned about composite functions at https://brainly.com/question/13502804

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