To find [tex]\( g(\sqrt{11}) \)[/tex] for the function [tex]\( g(x) = 6^x \)[/tex], follow the steps outlined below:
1. Identify the Function:
The function given is [tex]\( g(x) = 6^x \)[/tex].
2. Determine the Value of [tex]\( x \)[/tex]:
For this problem, [tex]\( x = \sqrt{11} \)[/tex]. We first need to compute [tex]\( \sqrt{11} \)[/tex].
3. Calculate [tex]\( \sqrt{11} \)[/tex]:
Using a calculator, find that [tex]\( \sqrt{11} \approx 3.3166247903554 \)[/tex].
4. Substitute [tex]\( x \)[/tex] into the Function:
Substitute [tex]\( x = \sqrt{11} \)[/tex] into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(\sqrt{11}) = 6^{\sqrt{11}}
\][/tex]
5. Compute [tex]\( 6^{\sqrt{11}} \)[/tex]:
Again, using a calculator, compute [tex]\( 6^{3.3166247903554} \)[/tex]:
[tex]\[
6^{3.3166247903554} \approx 380.921712113527
\][/tex]
6. Round to 4 Decimal Places:
Finally, round the result to four decimal places:
[tex]\[
380.921712113527 \approx 380.9217
\][/tex]
So, the value of [tex]\( g(\sqrt{11}) \)[/tex] rounded to four decimal places is [tex]\( \boxed{380.9217} \)[/tex].
