If the function m not-equals 0 has an inverse function, which statement must be true? B not-equals 0

Option a: m ≠ 0

Step-by-step 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.