Question

What is the function inverse of f(x)=50,000(.8)^x

Answer 1

I hope this helps you

Answer 2

Answer:

$f^{-1}(x)=\frac{\log(\frac{x}{50000})}{\log 0.8}$

Step-by-step explanation:

Given : The function $f(x)=50000(0.8)^x$

To find : The inverse of the given function?

Solution :

We write the given function as,

$y=50000(0.8)^x$

Taking log both side,

$\log y=\log 50000+\log (0.8)^x$

Apply logarithmic property, $\log a^x=x\log a$

$\log y=\log 50000+x\log 0.8$

$x=\frac{\log y-\log 50000}{\log 0.8}$

Now, interchange the value of x and y

$y=\frac{\log x-\log 50000}{\log 0.8}$

$f^{-1}(x)=\frac{\log x-\log 50000}{\log 0.8}$

$f^{-1}(x)=\frac{\log(\frac{x}{50000})}{\log 0.8}$