Let f(x)=(x+6)/5. Find f^-1(6)

Question

slaaibak · Answer

y = (x+6)/5

for the inverse:

x = (y+6)/5
5x - 6 = y

f^-1(16) = 5 * 16 - 6 = 74

slaaibak · Answer

Oh, f^-1(6).. I misread, sorry.

Then it's

f^-1(6) = 5 * 6 - 6 = 24

mertsj · Answer

Find f(6) and then switch the x and y

anonymous · Answer

okay when i find f(6) i get 12/5... then what?

mertsj · Answer

that means the ordered pair (6,12/5) is part of the function f  so (12/5,6) is a member of f^-1

slaaibak · Answer

Actually, you can set 6 = (x+6)/5

Then the x = f^-1(6)

but rather don't do that, since you have to fully grasp why that is possible

jamesj · Answer

@mertsj, Even so, that doesn't tell you the value of f^-1(6).

A simple way to think about this problem is the value or values of f^-1(6) is:

What are the value or values of x for which f(x) = 6?

Hence

f(x)=(x+6)/5 = 6.

Now solve for x.

slaaibak · Answer

$$f(x) = y \rightarrow x = f^{-1}(y)$$