Question

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

Answer 1

Note: Your question is missing some details. After a little research, I am able to find the complete question which is as follows:

If the function f(x) = mx + b has an inverse function, which statement must be true?

a) m=/0

b)  m = 0

c) b=/0

d )  b = 0

Answer:

The value of $m$ cannot be equal to 0. In other words,

$m\:\ne \:0$

Step-by-step explanation:

Considering the function

$f(x) = mx + b$

Lets find the inverse of this function.

Suppose

• $y=f\left(x\right)$

• $y=mx+b$

Lets exchange the variables $x$ and $y$ such as

$x=my+b$

Lets isolate the variable $y$

$my=x-b$

$y=\frac{x-b}{m}$

Suppose

$f\left(x\right)^{-1}=y$

As

$y=\frac{x-b}{m}$

So, inverse function is

$f\left(x\right)^{-1}=\frac{x-b}{m}$

As the denominator $m$ cannot be zero in the inverse function.

Thus, the value of $m$ cannot be equal to 0. In other words,

$m\:\ne \:0$

Keywords: function, inverse function

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