contestada

given the function
f(x)=0.5|x-4|-3, for what values of x is f(x)=7?

A. x=-24, x=16
B. x=-16, x=24
C. x=-1, x=9
D. x=1, x=-9

Respuesta :

7 = 0.5|x-4|- 3     add 3 to both sides: -
0.5|x-4| = 10        divide bs by 0,5:-
|x-4| = 20

either x - 4 = 20  or x - 4 = -20

this gives x = 24, x = -16
calculista

we have

[tex]f(x)=0.5\left|x-4\right|-3[/tex] -----> equation A

[tex]f(x)=7[/tex] -----> equation B

equate equation A and equation B

[tex]0.5\left|x-4\right|-3=7[/tex]

Adds [tex]3[/tex] boths sides

[tex]0.5\left|x-4\right|-3+3=7+3[/tex]

[tex]0.5\left|x-4\right|=10[/tex]

Multiply by [tex]2[/tex] boths sides

[tex]\left|x-4\right|=20[/tex]

we know that

The function absolute value has two solutions

Step 1

Find the first solution (positive case)

[tex]+(x-4)=20[/tex]

Adds [tex]4[/tex] boths sides

[tex]x-4+4=20+4[/tex]

[tex]x=24[/tex]

Step 2

Find the second solution (negative case)

[tex]-(x-4)=20[/tex]

Multiply by [tex]-1[/tex] boths sides

[tex](x-4)=-20[/tex]

Adds [tex]4[/tex] boths sides

[tex]x-4+4=-20+4[/tex]

[tex]x=-16[/tex]

therefore

the answer is the option B

[tex]x=-16, x=24[/tex]

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