Problem figuring out inverse function (looks easy but I'm confused)
Normally when you try to find f-1(x) you just switch the x and the y for example:
f(x) = x+3
x = y + 3
y = x - 3
f-1(x) = x- 3
but in the following problem:
"The formula C = 5/9(F-32), where F>= - 459.67, expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function and interpret it. What is the domain of the inverse function?"
The answer for the formula is F = 9/5*C + 32 which I also obtain if I solve for F (Note NOT switch the places of x (in this case F) and y (in this case C). My question is: why is this the case?
Could someone please explain the reasoning to me?
Thanks in advance!