How do you find the inverse of the function: $f(x)=-(5/3)x+10$

Question

I'm given the following function $$f(x)=-(5/3)x+10$$ and told to find the inverse. By using mymathlab help and typing in the wrong number multiple times it shows me the answer is $$f^{-1}(x)=-(3/5)x+6$$. How do you get to this answer? Do I need to switch $x$ and $y$ then solve for $x$?

Answer 1

set $f(x)=y$ and solve for $y$

$y=\frac{-5x}{3}+10\implies x=\frac{3(10-y)}{5}$ Thus $f^{-1}(x)=\frac{3(10-x)}{5}$

Answer 2

You would either switch x and y and then solve for y (in which case you get $y=-(3/5)x+6$)

Or you would leave x and y as is and solve for x (and get $x=-(3/5)y+6$)

Answer 3

The "forward mapping" is a mapping from $x$ to $f(x)=y$.

The "inverse mapping" is a mapping from $f(x)=y$ back to $x$.

So, rewrite $f(x)$ as $y$, since this will confuse you less.

Then, solve for $x$, getting $x = ... $.