Given the function f(x) = 0.5|x – 4| – 3, for what values of x is f(x) = 7?
x= -24, x = 16
x=-16, x = 24
x= -1, x= 9
x= 1, x= -9

Hence

x=24 and -16

Option B

Step-by-step explanation:

f(x) = 0.5|x – 4| – 3

we have to find the value of x for which f(x) = 7

hence we have to solve

7 = 0.5|x – 4| – 3 for x

adding 3 on both side

7+3= 0.5|x – 4|

10=0.5|x – 4|

dividing both sides by 0.50

=|x – 4|

a)

|x – 4|=20

x-4=20   for x-4≥0 or x≥4

adding 4 on both sides we get

x=24   for x-4≥0 or x≥4

b)

|x – 4|=-20

x-4=-20   for x-4≤0 or x≤4

adding 4 on both sides we get

x=-20+4   for x-4≤0 or x≤4

x=-16   for x-4≤0 or x≤4

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