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katrin2010 [14]
2 years ago
14

Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?

Mathematics
2 answers:
Radda [10]2 years ago
5 0
C
..............................
Advocard [28]2 years ago
3 0

Answer:  The correct option is

(C) x = -2, x = 6.

Step-by-step explanation:  We are given the following function :

f(x)=3|x-2|+6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to find the values of x for which f(x) = 18.

From equation (i), if f(x) = 18, we get

f(x)=18\\\\\Rightarrow 3|x-2|+6=18\\\\\Rightarrow 3|x-2|=18-6\\\\\Rightarrow 3|x-2|=12\\\\\Rightarrow |x-2|=\dfrac{12}{3}\\\\\Rightarrow |x-2|=4\\\\\Rightarrow x-2=4,~~~~~x-2=-4\\\\\Rightarrow x=6,~~~~~~~\Rightarrow x=-2.

Thus, the required solution is x = -2 and x = 6.

Option (C) is CORRECT.

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