Suppose a function f(.) is defined in the following way:
f(1) = 3
f(2) = 10
f(3) = 1
We could write this function as the set { (1,3), (2, 10), (3,1) }.
The inverse of f(.), let me call it g(.) can be given by:
g(3) = 1
g(10) = 2
g(1) = 3
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To find the inverse of a function, simply switch the variables x and y. So for the function y=7x+3, the inverse would be x=7y+3, or y=(x-3)/7.
The only trig functions i can think of with horizontal assymptotes are the inverse trig functions. and they go assymptotic for everytime the non-inverse function is equal to zero.
If its a fraction then we can change the numerators and denominators upside down .This is in case of fraction.
Take the derivative of the function and set it equal to zero. The solution(s) are your critical points.
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)