find the inverse function of f(x)=e^( 10(x-10) )

Question

jim_thompson5910 · Answer

Replace f(x) with y, and then swap x and y to get 

x = e^(10(y-10))


Now solve for y


x = e^(10(y-10))

ln(x) = 10(y-10)

ln(x) = 10y-100

ln(x)+100 = 10y

(1/10)(ln(x)+100) = y

y = (1/10)(ln(x)+100) 

y = ln(x)/10+10


So the inverse function is g(x) = ln(x)/10+10

anonymous · Answer

is this
$$e^{10x-100}$$

anonymous · Answer

yes that's the question

anonymous · Answer

then jim thompson has it

anonymous · Answer

ummm, haven't learned the "In" thing yet..what's that?

anonymous · Answer

inverse of 
$$e^x$$

jim_thompson5910 · Answer

the ln stands for the natural log. It's just a logarithm with base 'e'.

jim_thompson5910 · Answer

In other words, $$ln(x)=\log_{e}(x)$$

anonymous · Answer

ooo icic thank you so much

anonymous · Answer

if you haven't learned about log, this problem will make no sense

anonymous · Answer

can u write in the log form to show me?

jim_thompson5910 · Answer

Inverse function is $$f^{-1}(x)=\frac{\log_{e}(x)}{10}+10$$ using common log notation.

anonymous · Answer

ok this is how i did

x = 10(y-10)log e
x = 10ylog e- 100log e
x = 10( y log e- 10log e)
x/10 = y log e- 10log e
(x/10) + 10log e= ylog e
x/(10log e) +10=y

anonymous · Answer

can u check what I did wrong there? i just couldn't get the same answer like urs

jim_thompson5910 · Answer

When you took the log of the right side, you forgot to take the log of the left side as well. Also, the log e on the right side will turn into 1, which means that it essentially goes away.