find the inverse of the function, f(x)=x-1
given function:
y = x+1
Two step process
inverse function: (interchange x and y variables)
1.
x = y+1
2. solve new equation for y
y = x-1
so f^-1 (x) = x-1
Use the above two step method for finding any inverse if it exists.
To find the inverse of the function f(x) = x - 1, we need to swap the roles of x and y and then solve for y.
Step 1: Replace f(x) with y.
y = x - 1
Step 2: Swap x and y.
x = y - 1
Step 3: Solve for y.
x + 1 = y
Step 4: Swap y and f^-1(x).
f^-1(x) = x + 1
Therefore, the inverse of the function f(x) = x - 1 is f^-1(x) = x + 1.
To find the inverse of the function f(x) = x - 1, we need to interchange the roles of x and y and solve for y.
Step 1: Replace f(x) with y.
y = x - 1
Step 2: Swap x and y.
x = y - 1
Step 3: Solve for y.
x + 1 = y
So, the inverse of the function f(x) = x - 1 is f^(-1)(x) = x + 1.
To check if they are indeed inverses, you can compose the functions:
f(f^(-1)(x)) = (x + 1) - 1 = x
f^(-1)(f(x)) = (x - 1) + 1 = x
As you can see, when the original function and its inverse are composed, they cancel each other out, resulting in x. This confirms that they are inverses of each other.