Determine whether f and g are inverses of each other. f(x) = 5 − 8x; g(x) = 5 − x/8

Question

f(x) = 5 − 8x;   g(x) = 5 − x/8

A) f and g are inverses of each other

B) f and g are not inverses of each other.  

Answer 1

f= 5-8x

g= 5- x/8

are not inverses

Unless you meant g=(5-x)/8 and f=5-8x

as some people tend to leave out the parentheses

then they're inverses

let x=1

f(1)=-3

g(-3)= 1

g(f(x)) = x

g(f(1)) = 1

you start with x and then end with x when you do a composition of inverse functions

Answer 2

To determine whether f and g are inverses of each other, we need to check whether their compositions result in the identity function.

First, let's find f(g(x)):

f(g(x)) = f(5 - x/8) = 5 - 8(5 - x/8) = 5 - 40 + x = x - 35

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

g(f(x)) = g(5 - 8x) = 5 - (5 - 8x)/8 = 5 - 5/8 + x = x + 39/8

Since f(g(x)) = x - 35 and g(f(x)) = x + 39/8 are not equal to the identity function x, f and g are not inverses of each other.

Therefore, the correct answer is:

B) f and g are not inverses of each other.