SOLUTION: Solve for the inverse of the function f (x)= (-2/3)x+5

Question 1197091: Solve for the inverse of the function
f (x)= (-2/3)x+5
Found 3 solutions by ewatrrr, math_tutor2020, greenestamps:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi Solve for the inverse of the function: *Note: Notation f (x) =(-2/3)x+5 0r y = (-2/3)x+5 Replacing the y for x and x for y x = (-2/3)y + 5 Solving for y = (-3/2)(x-5) Wish You the Best in your Studies.

Answer by math_tutor2020(3822)   (Show Source): You can put this solution on YOUR website!

The inverse notation should be instead of

Otherwise I agree fully with the other tutor.

Answer by greenestamps(13219)   (Show Source): You can put this solution on YOUR website!

The response from the other tutor shows the traditional method for finding the inverse of a function: switch the x and y and solve for the new y.

For many relatively simple functions, an alternative which is often faster is to use the concept that an inverse function "un-does" what the function does.

For this example, the given function does this to the input:
(1) multiply by -2/3; and
(2) add 5

The inverse function, to undo that, needs to perform the opposite (inverse) operations in the opposite order:
(1) subtract 5; and
(2) divide by (-2/3) -- i.e., multiply by (-3/2)

ANSWER: y=(-3/2)(x-5)

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