Question

Let f(x) = e ^ (6x) and g(x) = 8in(x) Find and simplify g(f(- 2)) -96 -48 48 C B A

Answer 1

Answer: g(f(-2))=-96

Explanation:

`Given: \ f(x)=e^(6x)\ \ \ \ g(x)=8ln(x)\ \ \ \ g(f(-2))=?\\\\f(-2)=e^(6*(-2))\\\\f(-2)=e^(-12)\\\\Hence,\\\\g(f(-2))=8ln(e^(-12))\\\\g(f(-2))=8*(-12)\\\\g(f(-2))=-96`

Answer 2

-96

Explanation:

Given:

`\begin{cases}f(x)=e^(6x)\\ g(x)=8 \ln (x) \end{cases}`

To find g[f(-2)], substitute x = -2 into the function f(x):

`\implies f(-2)=e^(6 * -2)=e^(-12)`

Then substitute the function f(-2) in place of the x in function g(x):

`\implies g[f(-2)]=8 \ln \left(e^(-12)\right)`

`\textsf{Apply the power law}: \quad \ln x^n=n \ln x`

`\begin{aligned}\implies g[f(-2)]&=-12\cdot 8 \ln \left(e\right)\\&=-96 \ln \left(e\right)\end{aligned}`

Apply the log law: ln(e) = 1

`\begin{aligned}\implies g[f(-2)]&=-96 \ln \left(e\right)\\&=-96(1)\\&=-96\end{aligned}`

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As one calculation:

`\begin{aligned}g[f(-2)]&=8 \ln \left(e^(6 * -2)\right)\\& = 8 \ln \left(e^(-12)\right)\\& = -12 \cdot 8 \ln \left(e\right)\\& = -96(1)\\& = -96\end{aligned}`