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How do you find the inverse of $y = 2 x - 4$ $y=2x-4$ and is it a function?

1 Answer

Jun 20, 2016

inverse: $y = \frac{x + 4}{2}$ $y=(x+4)/2$
which is a function.

Explanation:

If $y = 2 x - 4$ $y=2x-4$
then
$XXX y + 4 = 2 x$ $color(white)("XXX")y+4=2x$
and
$XXX x = \frac{y + 4}{2}$ $color(white)("XXX")x=(y+4)/2$

Remember that $x$ $x$ and $y$ $y$ are arbitrary place holders and we could substitute any other variables in their place.
e.g. $x = \frac{y + 4}{2} \Leftrightarrow s = \frac{t + 4}{2}$ $x=(y+4)/2 hArr s=(t+4)/2$

however,it is common to express equations of this type with $y$ $y$ as the "dependent" variable (that is $y =$ $y=$ some expression based on the "independent" variable "x").

In this case we would write:
$XXX y = \frac{x + 4}{2}$ $color(white)("XXX")y=(x+4)/2$

Note that since this generates a single value for $y$ $y$ for any specific value of "x", this expression is a function.

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