Finding inverses Find the inverse function.

ƒ(x) = 3x - 4

Guida verificata passo dopo passo

Step 1: Understand the problem. We need to find the inverse of the function $ f(x) = 3x - 4 $. The inverse function, denoted as $ f^{-1}(x) $, is a function that 'reverses' the effect of $ f(x) $.

Step 2: Replace $ f(x) $ with $ y $. So, we have $ y = 3x - 4 $.

Step 3: Swap $ x $ and $ y $ to find the inverse. This gives us $ x = 3y - 4 $.

Step 4: Solve for $ y $. Add 4 to both sides to get $ x + 4 = 3y $.

Step 5: Divide both sides by 3 to isolate $ y $. This gives $ y = \frac{x + 4}{3} $. Thus, the inverse function is $ f^{-1}(x) = \frac{x + 4}{3} $.

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