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:
[tex]f(x)=0.5\times 3^x[/tex]
We are asked to find the value of the inverse function at 7.
i.e. we are asked to find:
[tex]f^{-1}(7)[/tex]
In other words we may say that we are asked to find the value of x when f(x)=7.
i.e.
[tex]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[/tex]
Hence, the value of [tex]f^{-1}(7)[/tex] is:
2.402
