Answer:
Option a: m ≠ 0
Explanation:
After a small online search, I've found that the complete question is:
If the function f(x) = m*x + b has an inverse function, which statement must be true?
a) m ≠ 0
b) m = 0
c) b ≠ 0
d) b = 0
Ok, if g(x) is an inverse of the function f(x), then:
g( f(x)) = x
f( g(x)) = x
Let's assume that f(x) = m*x + b has an inverse, and this inverse function is g(x).
Because f(x) is linear, g(x) is also linear, then:
g(x) = n*x + c
Let's find the values of A and B.
We know that:
f( g(x)) = x = m*(n*x + c) + b
then
x = m*n*x + m*c + b
Then we must have:
m*n = 1
(m*c + b) = 0
From the first equation m*n = 1
We get:
n = 1/m
The slope of the inverse function is one over the slope of the original function.
Because m is on the denominator, m can not be equal to zero (because a division by zero is not defined)
Then the correct option is the option a, m ≠ 0.