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Evaluate the function at the given values of [tex]$x$[/tex]. Round to 4 decimal places, if necessary.

[tex] g(x) = 6^x [/tex]

Part 1 of 4

[tex] g(-2) = 0.0278 [/tex]

Part 2 of 4

[tex] g(5.1) = 9301.8938 [/tex]

Part 3 of 4

[tex] g(\sqrt{11}) = 380.9217 [/tex]

Part 4 of 4

[tex] g(e) = \square [/tex]



Answer :

GinnyAnswer
To evaluate the function [tex]\( g(x) = 6^x \)[/tex] at [tex]\( x = e \)[/tex], follow these steps:

1. Understand the function: The function [tex]\( g(x) \)[/tex] is an exponential function where the base is [tex]\( 6 \)[/tex]. Therefore, [tex]\( g(x) = 6^x \)[/tex].

2. Identify the value of [tex]\( x \)[/tex]: For this part, we are asked to evaluate the function at [tex]\( x = e \)[/tex]. The constant [tex]\( e \)[/tex] (Euler's number) is approximately [tex]\( 2.71828 \)[/tex].

3. Compute [tex]\( 6^e \)[/tex]:
[tex]\[ g(e) = 6^e \approx 130.3870 \][/tex]

4. Round the result to 4 decimal places: The value of [tex]\( 6^e \)[/tex] rounded to four decimal places is [tex]\( 130.387 \)[/tex].

Therefore,
[tex]\[ g(e) = 130.387 \][/tex]

So, [tex]\( g(e) = 130.387 \)[/tex] when evaluated at [tex]\( x = e \)[/tex].

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