Find the inverse of the function ƒ(x) = 2x. Verify that ƒ(ƒ⁻¹(x)) = x and ƒ⁻¹(ƒ(x)) = x .

Guida verificata passo dopo passo

Step 1: To find the inverse of the function $ f(x) = 2x $, start by replacing $ f(x) $ with $ y $, so we have $ y = 2x $.

Step 2: Swap $ x $ and $ y $ to find the inverse function. This gives us $ x = 2y $.

Step 3: Solve for $ y $ in terms of $ x $. Divide both sides by 2 to get $ y = \frac{x}{2} $.

Step 4: Replace $ y $ with $ f^{-1}(x) $ to express the inverse function: $ f^{-1}(x) = \frac{x}{2} $.

Step 5: Verify the inverse by checking $ f(f^{-1}(x)) = x $ and $ f^{-1}(f(x)) = x $. Substitute $ f^{-1}(x) $ into $ f(x) $ and vice versa, and simplify to confirm both equal $ x $.

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