Find formula for inverse function of C = 5/9 * (F - 32)

[MarkSA]

Hello,

1) The formula C = 5/9 * (F - 32) where F >= -459.67, expresses the celsius temp C as a function of the fahrenheit temp F. Find a formula for the inverse function and interpret it. What is the domain of the inverse function?

I thought I understood how to find an inverse function, but I must not be doing this correctly. The answer for this question from the book is: F = 9/5 * C + 32
What confuses me is that it appears that they just rewrote the function. Multiply both sides by 9/5 and add 32 and you have their answer. How can this be the inverse function when it is the same as the original? I would have thought I would have to solve the equation for F (which is done above) and then swap the C and F to get the inverse function. This would give the inverse function as C = 9/5 * F + 32. But this is wrong?

Also, The domain of the inverse function should be equal to the range of the original function. But i'm not really sure how to find the range of the original function easily either. Any suggestions?

Thanks

 

[Deleted member 4993]

Re: Find the formula for the inverse function

C = 5/9 * (F-32)

solve for F

multiply both sides by 9/5

9/5 * C = F - 32

F = 9/5 * C + 32

Where you are getting in trouble is - interpretation of inverse function. your given function was:

f(x) = 5/9 *(x -32) ........where x = F

Your inverse function is:

f[sup:23gnw60o]-1[/sup:23gnw60o](x) = 9/5 * x + 32 ......where x = C (the "meaning" of 'x' has changed from 'F' to 'C' - while inverting))

The range of the original function is stated by the statement "F >= (-459.67)"

 

[MarkSA]

Re: Find the formula for the inverse function

Thanks I understand now.