The problem has been transcribed incorrectly.
It should read as follows:
Given f(x) = 3x-5, for what value of x does 2f(x) - 1 = f(3x-6)?
(A) 0
(B) 4
(C) 6
(D) 7
(E) 13
We can PLUG IN THE ANSWERS, which represent the value of x.
When the correct answer choice is plugged in, 2f(x) - 1 = f(3x-6).
Both the original function -- f(x) = 3x-5 -- and the equation above involve multiplication.
Generally, the smaller the value, the less the value will be affected by multiplication.
Implication:
2f(x) - 1 = f(3x-6) will likely be true for a relatively small value of x.
Answer choice B: x=4
2f(x) - 1:
f(x) = f(4) = 3*4 - 5 = 7.
Thus, 2f(x) - 1 = 2*7 - 1 = 13.
f(3x - 6):
f(3x - 6) = f(3*4 - 6) = f(6).
f(6) = 3*6 - 5 = 13.
Success!
2f(x) - 1 = f(3x-6) = 13.
The correct answer is
B.
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