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If f(x)=6^(1-x)-17, what is the value of f(3), to the nearest tenth (if necessary)? Answer:

If f(x)=61−x−17 f(x)=6^{1-x}-17 , what is the value of f(3) f(3) , to the nearest tenth (if necessary)?\newlineAnswer:

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Q. If f(x)=61−x−17 f(x)=6^{1-x}-17 , what is the value of f(3) f(3) , to the nearest tenth (if necessary)?\newlineAnswer:
  1. Substitute xx with 33: Substitute the value of xx with 33 in the function f(x)=6(1−x)−17f(x) = 6^{(1-x)} - 17.\newlinef(3)=6(1−3)−17f(3) = 6^{(1-3)} - 17
  2. Calculate exponent part: Calculate the exponent part of the function. 6(1−3)=6−26^{(1-3)} = 6^{-2}
  3. Evaluate 6−26^{-2}: Evaluate 6−26^{-2}. \newline6−2=1/62=1/366^{-2} = 1 / 6^2 = 1 / 36
  4. Subtract 1717: Subtract 1717 from the result of 6−26^{-2}. \newlinef(3)=136−17f(3) = \frac{1}{36} - 17
  5. Convert 1717 to fraction: Convert 1717 to a fraction with the same denominator as 136\frac{1}{36} to combine the terms.\newline17=17×(3636)=6123617 = 17 \times \left(\frac{36}{36}\right) = \frac{612}{36}
  6. Combine the fractions: Combine the fractions. f(3)=136−61236=−61136f(3) = \frac{1}{36} - \frac{612}{36} = -\frac{611}{36}
  7. Convert fraction to decimal: Convert the fraction to a decimal. f(3)=−61136≈−16.9722f(3) = -\frac{611}{36} \approx -16.9722
  8. Round to nearest tenth: Round the decimal to the nearest tenth. f(3)≈−17.0f(3) \approx -17.0

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