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f(x) = 2x – 2; find the inverse function

by lizzi3
(Bryant, Arkansas)











































Complete the inverse of F(x) below. If necessary, use the slash mark ( / ) for the division symbol. Do not include decimals or "F-1(y) =" in your answer.F(x) = 2x - 2 F^-1(y) = _________

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Oct 03, 2011
Inverse Function
by: Staff


Question:

Complete the inverse of F(x) below. If necessary, use the slash mark ( /) for the division symbol. Do not include decimals or "F-1(y) =" in your answer.F(x) = 2x - 2 F^-1(y) = _________


Answer:

f(x) = 2x - 2


solve for x

y = 2x - 2

y + 2 = 2x - 2 + 2

y + 2 = 2x + 0

y + 2 = 2x

(y + 2)/2 = 2x/2

(y + 2)/2 = x * (2/2)

(y + 2)/2 = x * (1)

(y + 2)/2 = x

x = (y + 2)/2

switch variables

y = (x + 2)/2

the inverse is:

y = (x + 2)/2

Now that you know what the inverse is, ask yourself this question: Is the inverse a function?

To answer this question, use the vertical line test.

To be a function, the equation must have only one y value for each x value.

The equation y = (x + 2)/2 passes the vertical line test. It is a function.


f⁻¹(x) = (x + 2)/2





the final answer is: f⁻¹(x) = (x + 2)/2, or f⁻¹(x) = (½)x + 1



Open the following link to view a graph of the function and the inverse function:


(1) If your browser is Firefox, click the following link to VIEW ; or if your browser is Chrome, Internet Explorer, Opera, or Safari (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/graph-function-and-inverse-2011-10-03.png


Thanks for writing.

Staff
www.solving-math-problems.com


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