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

Question

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

Lily Anderson · Accepted Answer

inverse: #y=(x+4)/2#
which is a function.

If #y=2x-4# then #color(white)("XXX")y+4=2x# and #color(white)("XXX")x=(y+4)/2# Remember that #x# and #y# are arbitrary place holders and we could substitute any other variables in their place. e.g. #x=(y+4)/2 hArr s=(t+4)/2# however,it is common to express equations of this type with #y# as the "dependent" variable (that is #y=# some expression based on the "independent" variable "x"). In this case we would write: #color(white)("XXX")y=(x+4)/2# Note that since this generates a single value for #y# for any specific value of "x", this expression is a function.

James Allen · Answer

undefined To find the inverse of the function $y = 2x - 4$, follow these steps:

1. Start with the original function: $y = 2x - 4$.
2. Swap the variables $x$ and $y$: $x = 2y - 4$.
3. Solve the equation for $y$.
4. Add 4 to both sides of the equation: $x + 4 = 2y$.
5. Divide both sides by 2: $\frac{x + 4}{2} = y$.

So, the inverse function is $y = \frac{x + 4}{2}$.

To determine if the inverse is a function, we need to check if each input $x$ corresponds to exactly one output $y$. Since each input value $x$ produces a unique output value $y$, and vice versa, the inverse function is indeed a function.