Question

Answer this question

Answer 1

Answer: OPTION B.

Explanation:

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

`f(x)=x^2-2x-8\\\\g(x)=(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)=(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)=(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)=(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)=(1)/(4)(0)-1=-1`

This is not the correct option.