Question

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

Answer 1

The inverse function of the function f(x) = mx + b can be determined by expressing the function in terms of x alone. hence, (y - b)/m = x. Then we exhange x and y, to result to (x - b)/m = y. In this case, m is not equal to zero. The answer to this problem hence is A>

Answer 2

we have

$f(x)=mx+b$

Find the inverse of f(x)

Let

$y=f(x)$

$y=mx+b$

Exchanges the variables x for y and y for x

$x=my+b$

isolate the variable y

$my=x-b$

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

Let

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

$f(x)^{-1}=\frac{x-b}{m}$ -----> inverse function

Hence

In the inverse function the denominator can not be zero, therefore the value of m can not be equal zero

the answer is the option

$m\neq 0$