Answered

Use a calculator to evaluate the function at the indicated values.

[tex]
\begin{array}{l}
g(x) = \left(\frac{6}{5}\right)^{5x} \\
g\left(-\frac{1}{2}\right) = \square \\
g(\sqrt{3}) = \square \\
g(-3) = \square \\
g\left(\frac{6}{5}\right) = \square
\end{array}
[/tex]



Answer :

GinnyAnswer
To evaluate the function \( g(x) \) at the given values, we need to substitute each value of \( x \) into the function \( g(x) = \left(\frac{6}{5}\right)^{5x} \) and calculate the result.

1. Evaluate \( g\left(-\frac{1}{2}\right) \):
[tex]\[ g\left(-\frac{1}{2}\right) = \left(\frac{6}{5}\right)^{5 \left(-\frac{1}{2}\right)} = \left(\frac{6}{5}\right)^{-2.5} \][/tex]
Using a calculator, we get:
[tex]\[ g\left(-\frac{1}{2}\right) \approx 0.633938145260609 \][/tex]

2. Evaluate \( g(\sqrt{3}) \):
[tex]\[ g(\sqrt{3}) = \left(\frac{6}{5}\right)^{5 \sqrt{3}} \][/tex]
Using a calculator, we get:
[tex]\[ g(\sqrt{3}) \approx 4.84986562514995 \][/tex]

3. Evaluate \( g(-3) \):
[tex]\[ g(-3) = \left(\frac{6}{5}\right)^{-15} \][/tex]
Using a calculator, we get:
[tex]\[ g(-3) \approx 0.0649054715188745 \][/tex]

4. Evaluate \( g\left(\frac{6}{5}\right) \):
[tex]\[ g\left(\frac{6}{5}\right) = \left(\frac{6}{5}\right)^6 \][/tex]
Using a calculator, we get:
[tex]\[ g\left(\frac{6}{5}\right) \approx 2.9859839999999993 \][/tex]

Thus, the evaluated values for the given function at the specific points are:
[tex]\[ g\left(-\frac{1}{2}\right) \approx 0.633938145260609 \][/tex]
[tex]\[ g(\sqrt{3}) \approx 4.84986562514995 \][/tex]
[tex]\[ g(-3) \approx 0.0649054715188745 \][/tex]
[tex]\[ g\left(\frac{6}{5}\right) \approx 2.9859839999999993 \][/tex]

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