To find the inverse of the function represented by y3x, we need to understand what ‘inverse’ means in this context. The inverse of a function switches the roles of the input and output. This means that if we have a function y = f(x), its inverse is x = f(y).
For the expression y3x, we assume it refers to a function where y is expressed in terms of x. Let’s rewrite this: if we have y = 3x, the goal is to solve for x in terms of y.
Start by swapping y and x:
- Replace y with x: x = 3y
Now solve for y:
- Divide both sides by 3: y = x/3
Thus, the inverse of the function y = 3x is y = (1/3)x. In summary, to find the inverse, we swapped the variables and isolated y, which led us to the final result.