Inverse of a function
The word inverse comes from the word invert which means opposite, upside down. Let f and g be two functions such that function g is inverse of function f. If function f produces an output y with input x, then putting y into inverse function g produces the output x, i.e. f(x) = y, and g(y) = x. So, if f and g are inverse functions, g(f(x) = x. Inverse of function f is denoted by f-1.
In other words, inverse of a function takes place when values of domain (x-values) and range (y-values) interchange. All values of the domain become the range and all values of the range become the domain.
Example
f(x) = {(1, 3), (2, 4), (3, 5), (4, 6)}
Inverse of f(x), f-1(x) = {(3, 1), (4, 2), (5, 3), (6, 4)}
Example
Find the inverse of y = x – 2
Follow the following steps to find the inverse of given function.
First solve for x
x = y + 2
Then switch x and y
y = x + 2
So, inverse function of x – 2 is x + 2
Example
Find inverse of y = 2x – 3.
First solve for x
y + 3 = 2x
x = (y + 3)/2
Now, switch x and y
y = (x + 3)/2
Hence, inverse of 2x – 3 is (x + 3)/2
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