How do you find the inverse of $x - 2 y = 5$ $x - 2y = 5$ and is it a function?

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Answer 1 · 2018-04-07T15:51:59

$f^{- 1} (x) = 2 x + 5$ $color(blue)(f^-1(x)=2x+5)$

$x - 2 y = 5$ $x-2y=5$

$y = \frac{1}{2} x - \frac{5}{2}$ $y=1/2x-5/2$

To find the inverse of this we express $x$ $x$ as a function of $y$ $y$ :

$x - 2 y = 5$ $x-2y=5$

$x = 2 y + 5$ $x=2y+5$

Substituting:

$y = x$ $y=x$

$y = 2 x + 5$ $y=2x+5$

$f^{- 1} (x) = 2 x + 5$ $color(blue)(f^-1(x)=2x+5)$

Yes this is a function.

For every input there is only one output.

The inverse of a function is always the function reflected in the line $y = x$ $y=x$

The graph below illustrates this:

enter image source here

How do you find the inverse of x−2y=5 x - 2y = 5 and is it a function?