Can you show me how we find the identity inverse function

Question

ScanSolve AI Tutor · Accepted Answer

To find the inverse function of a function, follow these steps: Step 1: Replace f(x) with y. Let the given function be y = f(x). Step 2: Swap x and y. Interchange the positions of x and y in the equation. This gives you x = f(y). Step 3: Solve for y. Rearrange the equation x = f(y) to isolate y. This will give you y in terms of x. Step 4: Replace y with f⁻¹(x). The expression you found for y is the inverse function, denoted as f⁻¹(x). For example, let's find the inverse of f(x) = 2x + 3. Step 1: y = 2x + 3; Step 2: x = 2y + 3 Step 3: x − 3 = 2y; y = (x − 3) / 2; Step 4: f⁻¹(x) = (x − 3) / 2

Can you show me how we find the identity inverse function

Step-by-step solution

Replace f(x) with y.

Swap x and y.

Solve for y.

Replace y with f⁻¹(x).

y = 2x + 3

x = 2y + 3

Step 7

f⁻¹(x) = (x - 3) / 2

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