Given f(x) = 2x+4, you found the inverse of this function is f^−1(x) = mx + b
swap x and y ... x = 2 y + 4 ... solve for y ... y = 1/2 x - 2
Mark f(x) as y
y = 2 x + 4
Replace all x with y and y with x
x = 2 y + 4
Subtract 4 to both sudes
x - 4 = 2 y
2 y = x - 4
Divide both sides by 2
y = x / 2 - 4 / 2
y = 1 / 2 x - 2
f ⁻¹ (x) = 1 / 2 x - 2
To find the inverse of the function f(x) = 2x + 4, we can follow these steps:
Step 1: Replace f(x) with y.
y = 2x + 4
Step 2: Interchange x and y.
x = 2y + 4
Step 3: Solve the equation for y.
x - 4 = 2y
(x - 4)/2 = y
y = (x - 4)/2
Therefore, the inverse of the function f(x) = 2x + 4 is given by f^−1(x) = (x - 4)/2.
To find the inverse of a function, you need to follow a few steps. Let's go through them using the given function f(x) = 2x + 4.
Step 1: Replace f(x) with y:
y = 2x + 4
Step 2: Swap x and y:
x = 2y + 4
Step 3: Solve the equation for y:
x - 4 = 2y
(x - 4)/2 = y
y = (1/2)x - 2
We have now obtained an equation in terms of y. However, to express the inverse as a function of x, we need to replace y with f^−1(x).
Therefore, the inverse function of f(x) = 2x + 4 is f^−1(x) = (1/2)x - 2, where m = 1/2 and b = -2.
It's important to note that the inverse of a function undoes the actions of the original function. So, if you apply f(x) followed by f^−1(x), or the other way around, you'll get back to the original input.