- #1
Champdx
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Homework Statement
f(x)=x+(5/x), how do i find f^-1(x)?
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The function f(x) is defined as x + (5/x). This means that for any given input value of x, the output of the function will be x added to the result of 5 divided by x.
To graph the function f(x), you can plot points by selecting different values for x and calculating the corresponding output values using the function formula. You can also use a graphing calculator or online graphing tool to plot the function.
f^-1(x) is the inverse function of f(x). It is a function that undoes the original function f(x) by swapping the input and output values. In other words, the input of f^-1(x) will be the output of f(x) and vice versa.
To find the inverse function f^-1(x), you can follow these steps:
1. Replace f(x) with y.
2. Switch the x and y variables in the equation, making it x = y + (5/y).
3. Solve the equation for y using algebraic manipulation.
4. Replace y with f^-1(x) to get the final inverse function.
The domain of f(x) is all real numbers except 0, as division by 0 is undefined. The range of f(x) is also all real numbers except 0, as the output of the function will never be 0 for any non-zero input value of x.