Question

question
suppose a function $f$ is defined by
$f(x)=mx + 2, x<0.$
if $f(m)=11$, what are the value(s) of $m$?
select the correct answer below:
$m = 11.$
$m=-3$
$m=pm3$
$m = 3.$

Explanation:

Step1: Substitute $x = m$ into the function

Since $f(x)=mx + 2$ for $x\lt0$ and we want to find $f(m)=11$, we substitute $x = m$ into the function to get $f(m)=m\times m+2=m^{2}+2$.

Step2: Set up the equation

Set $m^{2}+2 = 11$. Then, subtract 2 from both sides of the equation: $m^{2}=11 - 2=9$.

Step3: Solve for $m$

Taking the square - root of both sides, we have $m=\pm3$. But we need to consider the domain $x\lt0$ for the function $f(x)=mx + 2$. Since we are using the function $f(x)$ in the form where $x\lt0$ and $x = m$, we take $m=-3$ (because when $m = 3$, it does not satisfy the domain condition $x\lt0$ for the given piece - of the function).

Answer:

B. $m = - 3$