Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)
Answers: A) 0 B) 4 C) 6 D) 7 E) 13
explanations   We have the function f(x) = 3x – 5, and we want to some sophisticated algebra with it. Let’s look at the two sides of the prompt equation separately. The left side says: 2*[f(x)] – 1 —- this is saying: take f(x), which is equal to its equation, and multiply that by 2 and then subtract 1.   2*[f(x)] – 1 = 2*(3x – 5) – 1 = 6x – 10 – 1 = 6x – 11   The right side says f(3x – 6) — this means, take the algebraic expression (3x – 6) and plug it into the function, as discussed above in the section “How a mathematician things about a function.” This algebraic expression, (3x – 6), must take the place of x on both sides of the function equation.   f(3x – 6)= 3*[3x – 6] – 5 = 9x – 18 – 5 = 9x – 23   Now, set those two equal and solve for x:   9x – 23 = 6x – 11   9x = 6x – 11 + 23   9x = 6x + 12   9x – 6x = 12   3x = 12   x = 4   Answer = 4
<result>B</result>
Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6)