what is the inverse of f(x)=x/2+3

Question

abb0t · Answer

Solve for "x" in terms of "y".

reemii · Answer

write y=x/2+3 and do as abb0t said.
when you obtain "x=....stuff with y...", you actually found x='f-inverse'(y)

reemii · Answer

y=x/2+3 <-> y-3=x/2 <-> etc

anonymous · Answer

the inverse is y-3=x/2 ???

whpalmer4 · Answer

Your original function is $f(x) =y = x/2 + 3$Solve that for x in terms of y:
$$y = x/2+3$$$$y-3=x/2$$$$2(y-3)=x$$Now swap x and y:
$$2(x-3)=y$$$$f^{-1}(x)=2(x-3)$$

whpalmer4 · Answer

One interesting thing about inverse functions is that they look just like the original function reflected over the line y = x (a line going up and to the right at a 45 degree angle).  Here's an example (different functions, but no matter):

whpalmer4 · Answer

The purple line was the $f(x)$, the olive line was $f^{-1}(x)$, and the blue is $y=x$.  One way to check your work when doing inverse functions is to make a little graph and make sure the inverse and original functions make that reflection.