Question
evaluate f(x)=((3)/(4))^(x+2)-9 when x=0
Answers
Answered by
GPT-4o mini
To evaluate the function \( f(x) = \left( \frac{3}{4} \right)^{x+2} - 9 \) at \( x = 0 \), we can substitute \( x = 0 \) into the function:
\[
f(0) = \left( \frac{3}{4} \right)^{0+2} - 9
\]
This simplifies to:
\[
f(0) = \left( \frac{3}{4} \right)^{2} - 9
\]
Calculating \( \left( \frac{3}{4} \right)^{2} \):
\[
\left( \frac{3}{4} \right)^{2} = \frac{3^2}{4^2} = \frac{9}{16}
\]
Now substituting that back into the expression for \( f(0) \):
\[
f(0) = \frac{9}{16} - 9
\]
To perform the subtraction, convert 9 to a fraction with a denominator of 16:
\[
9 = \frac{144}{16}
\]
Now, substitute this back in:
\[
f(0) = \frac{9}{16} - \frac{144}{16} = \frac{9 - 144}{16} = \frac{-135}{16}
\]
Thus, the final result is:
\[
f(0) = -\frac{135}{16}
\]
\[
f(0) = \left( \frac{3}{4} \right)^{0+2} - 9
\]
This simplifies to:
\[
f(0) = \left( \frac{3}{4} \right)^{2} - 9
\]
Calculating \( \left( \frac{3}{4} \right)^{2} \):
\[
\left( \frac{3}{4} \right)^{2} = \frac{3^2}{4^2} = \frac{9}{16}
\]
Now substituting that back into the expression for \( f(0) \):
\[
f(0) = \frac{9}{16} - 9
\]
To perform the subtraction, convert 9 to a fraction with a denominator of 16:
\[
9 = \frac{144}{16}
\]
Now, substitute this back in:
\[
f(0) = \frac{9}{16} - \frac{144}{16} = \frac{9 - 144}{16} = \frac{-135}{16}
\]
Thus, the final result is:
\[
f(0) = -\frac{135}{16}
\]