This expression means to find the inverse function of f, where the output (y) is given and the input (x) is to be determined. In this case, the function is 1/(y+2/9)-1.
To solve for f-1(y), we need to isolate y on one side of the equation. First, we can multiply both sides by (y+2/9) to get 1-y-2/9 = x. Then, we can combine like terms and rearrange to get f-1(y) = -y-7/9.
The inverse function of 1/(y+2/9)-1 is -y-7/9.
To graph the inverse function, we can plot points by choosing values for y and solving for x using the inverse function. Then, we can connect the points to create a graph. Alternatively, we can also swap the x and y values of the original function and graph it, which will result in the same graph as the inverse function.
Finding inverse functions is important in science because it allows us to solve for unknown inputs when we know the output. This can be useful in many scientific fields, such as physics, chemistry, and biology, as it helps us understand the relationships between variables and make predictions based on data.