Question

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

Answer 1

I hope this helps you

Answer 2

`f^(-1)(x)=(\log((x)/(50000)))/(\log 0.8)`

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=(\log y-\log 50000)/(\log 0.8)`

Now, interchange the value of x and y

`y=(\log x-\log 50000)/(\log 0.8)`

`f^(-1)(x)=(\log x-\log 50000)/(\log 0.8)`

`f^(-1)(x)=(\log((x)/(50000)))/(\log 0.8)`