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If f(x)=2^(5x)+19, what is the value of f(-1), to the nearest tenth (if necessary)? Answer:

If f(x)=25x+19 f(x)=2^{5 x}+19 , what is the value of f(−1) f(-1) , to the nearest tenth (if necessary)?\newlineAnswer:

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Full solution

Q. If f(x)=25x+19 f(x)=2^{5 x}+19 , what is the value of f(−1) f(-1) , to the nearest tenth (if necessary)?\newlineAnswer:
  1. Substitute xx with −1-1: Substitute xx with −1-1 in the function f(x)=25x+19f(x) = 2^{5x} + 19.\newlinef(−1)=25(−1)+19f(-1) = 2^{5(-1)} + 19
  2. Calculate exponent part: Calculate the exponent part of the function.\newline25(−1)=2−52^{5(-1)} = 2^{-5}\newlineSince 2−52^{-5} means 11 over 22 raised to the power of 55, we calculate it as follows:\newline2−5=1/(25)=1/322^{-5} = 1 / (2^5) = 1 / 32
  3. Add 1919: Add 1919 to the result from Step 22.\newlinef(−1)=132+19f(-1) = \frac{1}{32} + 19\newlineTo add a fractions" target="_blank" class="backlink">fraction to a whole number, we can convert the whole number to a fraction with the same denominator.\newline19=19×(3232)=6083219 = 19 \times \left(\frac{32}{32}\right) = \frac{608}{32}\newlineNow we add the two fractions.\newlinef(−1)=(132)+(60832)=1+60832=60932f(-1) = \left(\frac{1}{32}\right) + \left(\frac{608}{32}\right) = \frac{1 + 608}{32} = \frac{609}{32}
  4. Convert to decimal: Convert the fraction to a decimal to find the nearest tenth. \newline609/32=19.03125609 / 32 = 19.03125\newlineRounded to the nearest tenth, this is 19.019.0.

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