Question

Given the function f(x) = 3|x – 2| + 6, for what values of x is f(x) = 18?
A. x = –2, x = –8
B. x = –2, x = –6
C. x = –2, x = 6
D. x = –2, x = 8

Answer 1

C
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Answer 2

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.