f(−1). So if we have to draw the graph of f-1, then we have to switch the positions of x and y in axes. Also, get more insights of how to solve similar questions and thus, develop problem-solving skills. Let’s dive in!In mathematics, an inverse function is a function (f) that inverts the particular function. So, we can restrict the domain anonymous two waysLets try first approach, if we restrict domain from 0 to infinity then we have the graph click to investigate thisWe have this graph and now when we check the graph for any value of y we are getting one value of x, in the same way, if we check for any positive integer of y we are getting only one value of x. Now, solve for \(y\).
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If we plot the graph our graph looks like this. Then f is invertible if there exists a function g from Y to X such that
g
(
f
(
x
)
)
=
x
{\displaystyle g(f(x))=x}
for all
{\displaystyle x\in X}
and
f
(
g
(
y
)
)
=
y
{\displaystyle f(g(y))=y}
for all
y
Y
{\displaystyle y\in Y}
. After drawing the straight line y = x, we observe that the straight line intersects the line of both of the functions symmetrically. . Specifically, if f is an invertible function with domain X and codomain Y, then its inverse f −1 has domain Y and image X, and the inverse of f −1 is the original function f.
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For the following exercises, find
f
−1
(x)
f
−1
(x) for each function. In the second case we did something similar. Notice the inverse operations are in reverse order of the operations from the original function. Okay, this is a mess. These algebraic functions are described below,Answer:An inverse function or also widely known as anti function is a function that reverses the result of given another function. Generally, the method of calculating an inverse is swapping of coordinates x and y.
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89 For instance, the inverse of the sine function is typically called the arcsine function, written as arcsin(x). .