Answer:
The answers are:
Graph: in the attached image
Inverse function: \(f^-^1(x)=5^x*2^x^-^3\)
Step-by-step explanation:
In order to get the graph with both functions, we have to determine the inverse function of \(y=log(8x)\)
The steps are:
- we have to free the "x" variable.
- Then we have to invert the "y" and "x" variables.
- Finally, the "y" variable is called \(f^-^1(x)\)
So, first, we applicate the next property:
If \(log_a(b)=c\), so \(a^c=b\)
\(y=log(8x)\\10^y=8x\\x=\frac{10^y}{8} \\x=(5*2)^y*2^-^3\\x=5^y*2^y*2^-^3\\x=5^y*2^y^-^3\)
Then, we invert the variables:
\(y=5^x*2^x^-^3\\f^-^1(x)=5^x*2^x^-^3\)
I have attached an image that shows the graph of both functions.
In red: \(y=log(8x)\)
In blue:\(f^-^1(x)=5^x*2^x^-^3\)
