This isn't right. All you have done is replace f(x) by y. The right side should have remained the same.Sweet_GirL said:Homework Statement
Find the inverse function of :
[tex]f(x)=e^x+e^{-x}+2[/tex] where [tex]x \geq 2[/tex]
Homework Equations
All what I did is :
[tex]y=e^x+e^{-x}+e[/tex]
Sweet_GirL said:The Attempt at a Solution
How in Earth can I solve this for x ?
An inverse function is a mathematical operation that "undoes" another function. It essentially reverses the input and output of a function. For example, if a function f(x) takes an input of x and gives an output of y, the inverse function would take an input of y and give an output of x.
Finding x for y in inverse functions allows us to solve equations and problems that involve a dependent variable (y) and an independent variable (x). It also helps us understand the relationship between the input and output of a function.
To find the inverse function of a given function, you can use the steps: (1) replace f(x) with y, (2) interchange the positions of x and y, (3) solve for y, and (4) replace y with f-1(x). It is important to note that not all functions have an inverse function.
The notation for inverse functions is f-1(x), where "f" represents the original function and the "-1" indicates the inverse operation. It is important to note that this does not mean the inverse of f multiplied by -1.
Inverse functions have various applications in fields such as physics, engineering, economics, and statistics. For example, they can be used to determine the speed of an object based on its position or to find the original value of a discounted price. They are also used in solving exponential and logarithmic equations.