Question

Consider a linear function f(x) = mx + b

(where the slope is not 0).
What is f-1(x)?
Use this formula to find the inverse of
h(x) = 2x - 9.

Answer 1

Answers:

`f^(-1)(x) = (x-b)/(m)\\\\`

and

`h^(-1)(x) = (x+9)/(2)\\\\`

See note below

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Step-by-step explanation:

First we replace f(x) with y. Then we swap x and y. Afterward, solve for y to determine the inverse function. The m value cannot be zero to avoid dividing by zero.

`f(x) = mx+b\\\\y = mx+b\\\\x = my+b\\\\x-b = my\\\\y = (x-b)/(m)\\\\f^(-1)(x) = (x-b)/(m)\\\\`

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For the formula h(x) = 2x-9, we see that m = 2 and b = -9

So the inverse for h(x) would be:

`h^(-1)(x) = (x-b)/(m)\\\\h^(-1)(x) = (x-(-9))/(2)\\\\h^(-1)(x) = (x+9)/(2)\\\\`

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Note: The function
`h^(-1)(x) = (x+9)/(2)\\\\` is the same as saying
`h^(-1)(x) = (1)/(2)x+(9)/(2)\\\\` or
`h^(-1)(x) = 0.5x+4.5\\\\`, so it will depend on what format your teacher wants.