Question

Which expression is equal to (f - g)(x)?

Answer 1

ANSWER

A. x-8

EXPLANATION

The given functions are:

$f(x) = {x}^{2} - 11x + 24$

We factor this to get,

$f(x) = (x - 8)(x - 3)$

and

$g(x) = x - 3$

$( \frac{f}{g} )(x) = \frac{f(x)}{g(x)}$

$( \frac{f}{g} )(x) = \frac{ {x}^{2} - 11x + 24}{x - 3} \: for\: x \ne3$

$( \frac{f}{g} )(x) = \frac{(x - 8)(x - 3)}{x - 3}$

Cancel the common factors to get,

$( \frac{f}{g} )(x) = x - 8$

Answer 2

Answer: OPTION A

Step-by-step explanation:

You need to divide the function f(x) by the function g(x):

Then:

$(\frac{f}{g})(x)=\frac{x^2-11x+24}{x-3}$

Now, you need to simplify:

Factor the numerator. Find two numbers whose sum be -11 and whose product be 24. Theses numbers are -8 and -3. Then you get:

$(\frac{f}{g})(x)=\frac{(x-8)(x-3)}{x-3}$

Remember that:

$\frac{a}{a}=1$

Then, you get that the expresson that is equal to  $(\frac{f}{g})(x)$ is:

 $(\frac{f}{g})(x)=(x-8)$