The inverse of f(x) =2x-1 is
Created: 2 years ago |
Updated: 2 months ago
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Caution: Inverse function (not inverse only)
Formula for inverse function:
1. y = f(x)
=> x => f^-1(y)
2. find x = something
Lets start:
y = f(x) = 2x-1
=> 2x = y+1
=> x = (y+1) / 2
=> f^-1(y) = (y+1) / 2
=> f^-1(x) = (x+1) / 2
The inverse of a function f(x) is denoted as f^(-1)(x) and is found by swapping the roles of x and y and then solving for y.
Given f(x) = 2x - 1, let's find its inverse:
- Swap x and y: x = 2y - 1.
- Solve for y: x + 1 = 2y.
- Divide by 2: (x + 1)/2 = y.
So, the inverse function is f^(-1)(x) = (x + 1)/2.
Therefore, the inverse of f(x) = 2x - 1 is (x + 1)/2
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