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If f(x)=(x^(2)+7)/(6x), what is the value of f(-7), to the nearest thousandth (if necessary)? Answer:

If f(x)=x2+76x f(x)=\frac{x^{2}+7}{6 x} , what is the value of f(−7) f(-7) , to the nearest thousandth (if necessary)?\newlineAnswer:

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Full solution

Q. If f(x)=x2+76x f(x)=\frac{x^{2}+7}{6 x} , what is the value of f(−7) f(-7) , to the nearest thousandth (if necessary)?\newlineAnswer:
  1. Substitute xx with −7-7: To find the value of f(−7)f(-7), we need to substitute xx with −7-7 in the function f(x)=x2+76xf(x)=\frac{x^{2}+7}{6x}.
  2. Calculate the numerator: Substitute xx with −7-7: f(−7)=((−7)2+7)/(6⋅−7)f(-7) = ((-7)^{2} + 7) / (6 \cdot -7).
  3. Calculate the denominator: Calculate the numerator: (−7)2+7=49+7=56(-7)^{2} + 7 = 49 + 7 = 56.
  4. Divide numerator by denominator: Calculate the denominator: 6×−7=−426 \times -7 = -42.
  5. Simplify the fraction: Now, divide the numerator by the denominator: 56−42\frac{56}{-42}.
  6. Convert fraction to decimal: Simplify the fraction: 56−42=−43\frac{56}{-42} = -\frac{4}{3}.
  7. Round to nearest thousandth: Convert the fraction to a decimal: −43≈−1.333-\frac{4}{3} \approx -1.333.
  8. Round to nearest thousandth: Convert the fraction to a decimal: −43≈−1.333-\frac{4}{3} \approx -1.333. Round the decimal to the nearest thousandth: −1.333-1.333 (it is already to the nearest thousandth).

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