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If f(x)=((1)/(4))^(x), what is the value of f(3) ? Choose 1 answer: (A) (3)/(4) (B) (1)/(16) (C) (1)/(64) (D) (1)/(256)

If f(x)=(14)x f(x)=\left(\frac{1}{4}\right)^{x} , what is the value of f(3) f(3) ?\newlineChoose 11 answer:\newline(A) 34 \frac{3}{4} \newline(B) 116 \frac{1}{16} \newline(C) 164 \frac{1}{64} \newline(D) 1256 \frac{1}{256}

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Full solution

Q. If f(x)=(14)x f(x)=\left(\frac{1}{4}\right)^{x} , what is the value of f(3) f(3) ?\newlineChoose 11 answer:\newline(A) 34 \frac{3}{4} \newline(B) 116 \frac{1}{16} \newline(C) 164 \frac{1}{64} \newline(D) 1256 \frac{1}{256}
  1. Identify function and value: Identify the function and the value of xx for which we need to find f(x)f(x).\newlineWe have the function f(x)=(14)xf(x) = (\frac{1}{4})^x and we need to find the value of f(3)f(3).
  2. Substitute xx with 33: Substitute xx with 33 in the function f(x)f(x).f(3)=(14)3f(3) = \left(\frac{1}{4}\right)^3
  3. Calculate (14)3(\frac{1}{4})^3: Calculate the value of (14)3(\frac{1}{4})^3.\newline(14)3=14×14×14=164(\frac{1}{4})^3 = \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} = \frac{1}{64}
  4. Match calculated value: Match the calculated value with the given choices.\newlineThe calculated value of f(3)f(3) is 164\frac{1}{64}, which corresponds to choice (C).

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