Question

In Desmos, graph y= (-5x, 4y)

1. state the domain and range of the original function
2. state the domain and range of the inverse function
3. the inverse reflects over?

Answer 1

Given,

$y= (-5x, 4y)$

We can write the given function as

$y=-5x$ and $x= 4y$

in the above we can see that the dark red line is representing $y=-5x$ and dark blue line is representing $4y=x$

Both the function is a linear function so the domain and range of both the function be,

$D=(-\infty,\infty)$

$R=(-\infty,\infty)$

c)

$y=-5x$

Now, taking the inverse,

$x=\frac{-y}{5}$

$f^{-1}(x)=\frac{-x}{5}$

Similarly for the second function,

$y=\frac{x}{4}$

taking the inverse,

$f^{-1}(x)=4x$

As both the function are linear, and a linear function will be invertible as long as it's non-constant.