Answer:
The value of the given expression is:
2.402
Step-by-step explanation:
We are given a exponential function f(x) which is represented by:
\(f(x)=0.5\times 3^x\)
We are asked to find the value of the inverse function at 7.
i.e. we are asked to find:
\(f^{-1}(7)\)
In other words we may say that we are asked to find the value of x when f(x)=7.
i.e.
\(0.5\times 3^x=7\\\\3^x=\dfrac{7}{0.5}\\\\3^x=14\\\\x\log 3=\log 14\\\\x=\dfrac{\ln 14}{\ln 3}\\\\x=2.402\)
Hence, the value of \(f^{-1}(7)\) is:
2.402
