Question

if the function $f(x) = mx + b$ has an inverse function, which statement must be true?
$m \
eq 0$
$m = 0$
$b \
eq 0$
$b = 0$

Explanation:

Step1: Recall inverse function condition

A function has an inverse if and only if it is one-to-one (strictly monotonic, no repeated y-values).

Step2: Analyze linear function behavior

For $f(x)=mx+b$:

• If $m=0$, $f(x)=b$, a constant function (not one-to-one, fails horizontal line test).
• If $m

eq0$, the function is strictly increasing/decreasing (one-to-one, passes horizontal line test).

• The value of $b$ does not affect whether the function is one-to-one; it only shifts the line vertically.

Answer:

$m
eq0$