how to find the inverse of a function
switch x and y and solve for y
To find the inverse of a function, follow these steps:
1. Replace f(x) with y: y = f(x)
2. Swap x and y: x = f(y)
3. Solve for y: y = f-1(x)
For example, let’s find the inverse of the function f(x) = 2x + 3.
1. Replace f(x) with y: y = 2x + 3
2. Swap x and y: x = 2y + 3
3. Solve for y:
x = 2y + 3
x – 3 = 2y
(y = x – 3)/2
Thus, the inverse of f(x) = 2x + 3 is f-1(x) = (x – 3)/2.
It is important to note that not all functions have inverses, and some functions may have more than one inverse. Also, the domain and range of the inverse function may differ from that of the original function, so it is important to check for any restrictions on the domain or range.
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