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Use the following function rule to find f(77)f(77).\newlinef(x)=6102−xf(x) = 6\sqrt{102 - x}\newlinef(77)=f(77) = _____

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Full solution

Q. Use the following function rule to find f(77)f(77).\newlinef(x)=6102−xf(x) = 6\sqrt{102 - x}\newlinef(77)=f(77) = _____
  1. Identify Function & Input: Identify the function and the input value.\newlineWe are given the function f(x)=6102−xf(x) = 6\sqrt{102 - x} and we need to find the value of f(77)f(77).
  2. Substitute Input: Substitute the input value into the function.\newlineTo find f(77)f(77), we replace xx with 7777 in the function:\newlinef(77)=6102−77f(77) = 6\sqrt{102 - 77}
  3. Perform Subtraction: Perform the subtraction inside the square root.\newlineCalculate the value inside the square root: 102−77=25102 - 77 = 25
  4. Evaluate Square Root: Evaluate the square root.\newlineSince the square root of 2525 is 55, we have:\newline25=5\sqrt{25} = 5
  5. Multiply by 66: Multiply the result by 66. Now, multiply the square root by 66 to find f(77)f(77): f(77)=6×5f(77) = 6 \times 5
  6. Calculate Final Result: Calculate the final result. f(77)=30f(77) = 30

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