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Given the function [tex]f(x) = 4|x – 5| + 3[/tex], for what values of x is [tex]f(x) = 15[/tex]?

A. x = 2, x = 8
B. x = 1.5, x = 8
C. x = 2, x = 7.5
D. x = 0.5, x = 7.5

Answer :

Mode function is the function that keeps the value of the function between the range of positive to negative number which is equal to the result of given function. The value x is 2 and 8 for the given function and it can be written as,

[tex]x=2\;\;\; \vee \;\;\;x=8[/tex]

Given information-

The given function in the problem is-

[tex]f(x) = 4|x- 5| +3[/tex]

The value of x has to be find out for the function,

[tex]f(x)=15[/tex]

Mode function-

Mode function is the function that keeps the value of the function between the range of positive to negative number which is equal to the result of given function.

As both the given function are function of x and equal. Thus compare both the function to find the value of x.

Thus,

[tex]4|x- 5| +3=15[/tex]

Substract with 3 both the sides,

[tex]\begin{aligned}\\4|x- 5| +3-3&=15-3\\4|x- 5| &=12\\\end[/tex]

Divide both side by 4 and solve further,

[tex]|x- 5| &=3[/tex]

As the result of the above mode function is equal to the positive 3 and negative 3. thus,

[tex]x-5=-3\\x-5=3[/tex]

Thus the value x is 2 and 8 for the given function and it can be written as,

[tex]x=2\;\;\; \vee \;\;\;x=8[/tex]

Learn more about the algebraic functions here;

https://brainly.com/question/953809

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Rewritten by : Jeany

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