Question

Answer this question

Answer 1

Answer:  OPTION B.

Step-by-step explanation:

We have the following functions f(x) and g(x):

$f(x)=x^2-2x-8\\\\g(x)=\frac{1}{4}x-1$

In order to find for which values of "x" $f(x)=g(x)$, we can check each option given:

OPTION A

Substitute $x=-1.75$ into the function f(x) and evaluate:

$f(-1.75)=(-1.75)^2-2(-1.75)-8=-1.4375$

 Substitute $x=-1.75$ into the function g(x) and evaluate:

$g(-1.75)=\frac{1}{4}(-1.75)-1=-1.4375$

Substitute $x=-1.438$ into the function f(x) and evaluate:

$f(-1.438)=(-1.438)^2-2(-1.438)-8=-3.0561$

Substitute $x=-1.438$ into the function g(x) and evaluate:

$g(-1.438)=\frac{1}{4}(-1.438)-1=-1.3595$

This is not the correct option.

OPTION B

We already know that:

$f(-1.75)=-1.4375$

$g(-1.75)=-1.4375$

Substitute $x=4$ into the function f(x) and evaluate:

$f(4)=(4)^2-2(4)-8=0$

Substitute $x=4$ into the function g(x) and evaluate:

$g(4)=\frac{1}{4}(4)-1=0$

This is the correct option.

OPTION C

We already know that:

 $f(-1.438)=-3.0561$

 $g(-1.438)=-1.3595$

Therefore, this is not the correct option.

OPTION D

We already know that:

$f(4)=0$

$g(4)=0$

Substitute $x=0$ into the function f(x) and evaluate:

$f(0)=(0)^2-2(0)-8=-8$

Substitute $x=0$ into the function g(x) and evaluate:

$g(0)=\frac{1}{4}(0)-1=-1$

This is not the correct option.