Evaluate the function f(x)=3x^2 - 9x + 6 at the indicated values of f(x/2) and f(x^2)

Question

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Answer 1

f(x/2) and f(x^2) simply are instructions telling us to evaluate f(x) at the quantities x/2 and x^2, respectively. Ordinarily, we might expect that the x in f(x) is a real number (any number on the real number line), but x/2 and x^2 are such arbitrary numbers that the function takes in and maps to its output. The procedure for determining the output is simply evaluating the function at x/2 and x^2 by plugging them into the function. After that its simple algebra to simplify the equation output.

Answer 2

When considering a variation in the inputs of a function, f(x), typically what is normally provided for x becomes the new substituted variable. For example when we say f(2), we are really saying that f(x2) = 3×(2)²-9×2+6 = 12-18+6 = 0. So for f(x/2) = 3×(x/2)^2-9×(x/2)+6 = 3/4×(x)^2-9/2x+6

Therefore, for f(x²)= 3×(x²)²-9×x²+6 = 3x⁴-9x²+6