How do you verify if f(x)=7x; g(x)=1/7x are inverse functions?

2 Answers
Apr 14, 2017

See below.

Explanation:

We swap the places of x and y (in this case, f(x)).

y=7x

x=7y

1/7x=y, which is g(x), so the functions are inverses of each other.

Apr 15, 2017

Here's another way of going at it. Apply the identity f(f^-1(x)) = x.

f(f^-1(x)) = f(g(x)) = 7(1/7x) = x color(green)(√)

Check the other way:

f^-1(f(x)) = g(f(x)) = 1/7(7x) = x color(green)(√)

Hence, f(x) and g(x) are indeed inverses of each other.

Hopefully this helps!