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If
f(x)=3^(3x)+14, what is the value of
f(-1), to the nearest thousandth (if necessary)?
Answer:

If $f(x)=3^{3 x}+14$ , what is the value of $f(-1)$ , to the nearest thousandth (if necessary)? $\newline$ Answer:

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Solve exponential equations using logarithms

Full solution

Q. If

f(x)=3^{3 x}+14

, what is the value of

f(-1)

, to the nearest thousandth (if necessary)?

\newline

Answer:

Substitute $x$ with $-1$ : To find the value of $f(-1)$ , we need to substitute $x$ with $-1$ in the function $f(x) = 3^{3x} + 14$ . $\newline$ $f(-1) = 3^{3*(-1)} + 14$
Calculate the exponent: Now we calculate the exponent part: $3*(-1) = -3$ . So, $f(-1) = 3^{-3} + 14$
Calculate $3^{-3}$ : Next, we calculate $3^{-3}$ . Since a negative exponent means the reciprocal of the base raised to the positive exponent, we have $3^{-3} = \frac{1}{3^3}$ . $\newline$ $f(-1) = \frac{1}{3^3} + 14$
Calculate $3^3$ : Now we calculate $3^3$ which is $3*3*3 = 27$ . $\newline$ So, $f(-1) = \frac{1}{27} + 14$
Perform the division: We then perform the division: $\frac{1}{27}$ is approximately $0.037$ (rounded to three decimal places). $\newline$ $f(-1) = 0.037 + 14$
Add to get $f(-1)$ : Finally, we add $0.037$ to $14$ to get the value of $f(-1)$ . $\newline$ $f(-1) = 14.037$

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