Question

Determining whether two functions are inverses of each other.

Answer 1

f(x) = 6x + 5
g(x) = 6x - 5
f(g(x)) = 6(6x - 5) + 5 = 36x - 30 + 5 = 36x - 25
g(f(x)) = 6(6x+ 5) - 5 = 36x + 30 - 5 = 36x + 25

f and g are not inverse of each other.

Answer 2

f and g are not inverse of each other.

Explanation:

If the two functions are inverses of each other, then f(g(x)) = g(f(x))

We are given two functions:

f(x) = 6x + 5

g(x) = 6x - 5

Let's find f(g(x)) and g(f(x))

f(g(x)) = f(6x - 5)

= 6(6x - 5) + 5

= 36x - 30 + 5

f(g(x)) = 36x - 25

Now let's find g(f(x))

g(f(x)) = g(6x + 5)

= 6(6x + 5) - 5

= 36x + 30 - 5

g(f(x))= 36x + 25

We see that f(g(x)) ≠ g(f(x))

Therefore, f and g are not inverse of each other.