Answer: OPTION B.
Step-by-step explanation:
We have the following functions f(x) and g(x):
[tex]f(x)=x^2-2x-8\\\\g(x)=\frac{1}{4}x-1[/tex]
In order to find for which values of "x" [tex]f(x)=g(x)[/tex], we can check each option given:
OPTION A
Substitute [tex]x=-1.75[/tex] into the function f(x) and evaluate:
[tex]f(-1.75)=(-1.75)^2-2(-1.75)-8=-1.4375[/tex]
Substitute [tex]x=-1.75[/tex] into the function g(x) and evaluate:
[tex]g(-1.75)=\frac{1}{4}(-1.75)-1=-1.4375[/tex]
Substitute [tex]x=-1.438[/tex] into the function f(x) and evaluate:
[tex]f(-1.438)=(-1.438)^2-2(-1.438)-8=-3.0561[/tex]
Substitute [tex]x=-1.438[/tex] into the function g(x) and evaluate:
[tex]g(-1.438)=\frac{1}{4}(-1.438)-1=-1.3595[/tex]
This is not the correct option.
OPTION B
We already know that:
[tex]f(-1.75)=-1.4375[/tex]
[tex]g(-1.75)=-1.4375[/tex]
Substitute [tex]x=4[/tex] into the function f(x) and evaluate:
[tex]f(4)=(4)^2-2(4)-8=0[/tex]
Substitute [tex]x=4[/tex] into the function g(x) and evaluate:
[tex]g(4)=\frac{1}{4}(4)-1=0[/tex]
This is the correct option.
OPTION C
We already know that:
[tex]f(-1.438)=-3.0561[/tex]
[tex]g(-1.438)=-1.3595[/tex]
Therefore, this is not the correct option.
OPTION D
We already know that:
[tex]f(4)=0[/tex]
[tex]g(4)=0[/tex]
Substitute [tex]x=0[/tex] into the function f(x) and evaluate:
[tex]f(0)=(0)^2-2(0)-8=-8[/tex]
Substitute [tex]x=0[/tex] into the function g(x) and evaluate:
[tex]g(0)=\frac{1}{4}(0)-1=-1[/tex]
This is not the correct option.
