6
y = 3x - 3
y + 3 = 3x
y/3 + 1 = x
So the inverse function is x = y/3 + 1
y=3x-3
y+3=3x
y+1/3=
If f(x)=y, then the inverse function solves for y when x=f(y). You may have to restrict the domain for the inverse function to be a function. Use this concept when finding the inverse of hyperbolic functions.
10
First, this function is strictly increasing on the entire real line, so an inverse exist on the entire real line. We define inverse of function f, denoted f^-1 such that if y = f(x) then f^-1(y) = x Or to find the inverse, all is needed is to isolate x in terms of y. In this case, y = 7x + 2 7x = y - 2 x = (y - 2)/7 So the inverse is x = (y - 2)/7 What? You don't like function in terms of y? Well, they are just meaningless variables anyway, you can write whatever, in particular the inverse is y = (x - 2) / 7 (the x, y here are independent with the x, y above. If you are getting confused, write b = (a - 2)/7 where b is a function of a)
A reciprocal function will flip the original function (reciprocal of 3/5 is 5/3). An inverse function will change the x's and y's of the original function (the inverse of x<4,y>8 is y<4, x>8). Whenever a function is reflected over the line y=x, the result is the inverse of that function. The y=x line starts at the origin (0,0) and has a positive slope of one. All an inverse does is flip the domain and range.
Let N= inverse of Y Given 1/Y=4 ---> Y=1/4 inverse of 1/4 ---> 1/(1/4)=4 N=inverse of Y=4
log5x
Because the inverse of a function is what happens when you replace x with y and y with x.
Assuming that b > 0, it is an inverse power function or an inverse exponential function.
Direct
To find the inverse of a function, you replace x with y and y with x. Here, y=2x-4 would become x=2y-4. Now, we solve for y. 2y=x+4. y=(x/2)+4, and that is the inverse equation.
Since the equation is in terms of x, you need to switch the x's and y's, and then solve it for y again. y=3x^3 --> x=3y^3 --> y=(x/3)^(1/3)
Simply stated, the inverse of a function is a function where the variables are reversed. If you have a function f(x) = y, the inverse is denoted as f-1(y) = x. Examples: y=x+3 Inverse is x=y+3, or y=x-3 y=2x+5 Inverse is x=2y+5, or y=(x-5)/2
x=y is the identity. It is its own inverse. So the inverse is y=x.
1
To find the inverse simply switch the x's with the y's so... inverse of y=x is x=y
Assuming the domain and range are both the real numbers (or rationals): Yes, it is 1 to 1 Yes, it is onto and the inverse is x = (y-3)/4
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()