Inverse Function Inverse Function In mathematics, an inverse function is a function that undoes another function: If an input x into the function ƒ produces an output y, then putting y into the inverse function g produces the output x, and vice versa. i.e., ƒ(x)=y, and g(y)=x. More directly, g(ƒ(x))=x, meaning g(x) composed with ƒ(x) leaves x unchanged. A function ƒ that has an inverse is called invertible; the inverse function is then uniquely determined by ƒ and is denoted by ƒ−1 (read f inverse, not to be. Inverse function is the backtrack approach of a function. If there is a function with input ‘p’ and its giving the output as ‘q’ then the function which has input as ‘q’ and gives the output as ‘p’, that function will be called as the inverse function of a given function. When we perform a task and get an output, then if we treat that output as input and get the initial input value, this works as inverse function. Function and the inverse of a function share a relation together. We can show that relation as :
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f(g(p)) = g(f(p)) = q In this if we inverse the function we will get the same result as q. We can find the inverse just by the swapping of value p and q and we get a new relation which represents the inverse of a function. But we have to note that it is not necessary that an inverse is always a function. Let us assume that we are given a function say f(p) and getting the output q then we will denote the inverse function with q input as f-1 (q). For understanding the inverse function in a better manner let us take another example. Assume a function f(p)=2p+6 then what will be its inverse function let’s take a look: f(p) = 2p + 6 p ----> 2*p --- > 2*p + 6 This function will be processed in this manner. For calculating its inverse just does the opposite of each task or inverse of each task like replace addition with subtraction and multiplication with division. f-1(q) will be (q - 6)/2
< -----
q-6
<---- q
So the inverse function f-1(q) of function f(p) is: f-1(q) = (q - 6)/2
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Mathematics approach: step 1: step 2:
f(p) = 2p + 6 Put q at the place of f(p) q = 2p + 6
step 3: Take Integer value at left side q - 6 = 2p step 4: Divide left side by the coefficient of p (q - 6) /2 = p Step 5:
p = (q - 6) / 2
Step 6: Put f-1(q) at the place of p. f-1(q) = (q - 6) /2 This is the all about inverse of function.
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