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If f(x)=(3)/(14-x^(2)), what is the value of f(-6), to the nearest thousandth (if necessary)? Answer:

If f(x)=314−x2 f(x)=\frac{3}{14-x^{2}} , what is the value of f(−6) f(-6) , to the nearest thousandth (if necessary)?\newlineAnswer:

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Full solution

Q. If f(x)=314−x2 f(x)=\frac{3}{14-x^{2}} , what is the value of f(−6) f(-6) , to the nearest thousandth (if necessary)?\newlineAnswer:
  1. Substitute xx with −6-6: Substitute xx with −6-6 in the function f(x)=314−x2f(x) = \frac{3}{14-x^2}.
    f(−6)=314−(−6)2f(-6) = \frac{3}{14-(-6)^2}
  2. Calculate value of (−6)2(-6)^2: Calculate the value of (−6)2(-6)^2.\newline(−6)2=36(-6)^2 = 36
  3. Substitute 3636 into function: Substitute 3636 into the function.f(−6)=314−36f(-6) = \frac{3}{14-36}
  4. Perform subtraction in denominator: Perform the subtraction in the denominator. 14−36=−2214 - 36 = -22
  5. Calculate value of f(−6-6): Calculate the value of f(−6)f(-6).f(−6)=3−22f(-6) = \frac{3}{-22}
  6. Simplify fraction to decimal: Simplify the fraction to get the decimal value. f(−6)≈3−22≈−0.136363636…f(-6) \approx \frac{3}{-22} \approx -0.136363636\ldots
  7. Round result to nearest thousandth: Round the result to the nearest thousandth. f(−6)≈−0.136f(-6) \approx -0.136

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