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y = 5x - 4
y + 4 = 5x
x = (y + 4)/5
Conventionally, the x and y are then swapped in the expression of the inverse function.
So, the inverse function is y = (x + 4)/5
The inverse of the function y = x is denoted as y = x. The inverse function essentially swaps the roles of x and y, so the inverse of y = x is x = y. In other words, the inverse function of y = x is the function x = y.
Follow this example. f(x) = (x+3)/5 To find its inverse, write y=f(x) y= (x+3)/5 Interchange x and y x = (y+3)/5 solve for y in terms of x 5x=y+3 y=5x-3 The inverse of f(x) is f^-1(x) = 5x-3
A function that, given X, will produce Y has an inverse function that will take Y and produce X. More formally:If f(x)=y, then f-1(y)=xWhere f-1() denotes the inverse function of f()
The inverse of a linear function is always a linear function. There are a few ways to approach this.To think about it, you can imagine flipping the x and y axes. Essentially this equates to turning the graph of the linear function on its side to reveal the new inverse function which is still a straight line.More rigorously, the linear function y = ax + b has the inverse equation x = (1/a)y - (b/a). This is a linear function in y.
The inverse of the function y = 9x is x/9.