SOLUTION: Let f(x) =2x-3 find f-1, ff-1(x), ff-1(4)

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Question 1191974: Let f(x) =2x-3 find f-1, ff-1(x), ff-1(4)
Found 2 solutions by Solver92311, greenestamps:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


To find the inverse of a function :

1. Replace with a dependent variable such as

2. Solve for the independent variable () in terms of the dependent variable.

3. Interchange the variables, that is, swap for and for

4. Replace the dependent variable with


John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


f(x)=2x-3

(1) Find f^(-1)(x)

There is a simple method for finding the inverse of a simple function like this, using the idea that an inverse function "un-does" what the function does.

The given function does the following to the input:
.. multiply by 2; and
.. subtract 3

The inverse function, to undo that the function does, must perform the opposite operations in the opposite order:
.. add 3; and
.. divide by 2

ANSWER: f^(-1)(x) = (x+3)/2

(2) By the definition of an inverse function, f(f^(-1)(x))=x

(3) Likewise, f(f^(-1)(4))=4