How To Find The Inverse Of An Equation In Mathematics: A Step-By-Step Guide

What is the inverse of the equation y = x + 4 ?

y = x – 4

To find the inverse of the equation y = x + 4, we need to solve for x in terms of y.

Here is the process to find the inverse:

Step 1: Replace y with x and x with y.
x = y + 4

Step 2: Solve for y.

Subtract 4 from both sides:
x – 4 = y

Step 3: Rewrite the equation with y on the left-hand side.

y = x – 4

The inverse of the equation y = x + 4 is y = x – 4.

We can verify this by using function composition:

If we apply the original function followed by the inverse function, we should get back the input value:

f(x) = x + 4
f^-1(x) = x – 4

(f^-1 o f)(x) = f^-1(f(x))
= f^-1(x + 4)
= (x + 4) – 4
= x

Similarly, if we apply the inverse function followed by the original function, we should also get back the input value:

(f o f^-1)(x) = f(f^-1(x))
= f(x – 4)
= (x – 4) + 4
= x

Therefore, y = x – 4 is the inverse of the equation y = x + 4.

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