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):
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.
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)
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