Inverse of a Linear Function

Step‑by‑step algebra solver + graphical reflection about \( y = x \). Generate random linear functions, see detailed algebraic solutions, and visualize how a function and its inverse are symmetric across the line \( y = x \).

📐 Interactive Calculator • Purple Theme

✨ A linear function \( f(x) = ax + b \) (with \( a \neq 0 \)) has an inverse \( f^{-1}(x) = \frac{x - b}{a} \). Swap \(x\) and \(y\) and solve. Below, generate random exercises, see detailed steps, and visualize symmetry.
\( f(x) = 3x - 2 \)

📖 Step-by-Step Solution

STEP 1: Replace \(f(x)\) by \(y\)
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STEP 2: Solve for \(x\)
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STEP 3: Interchange \(x\) and \(y\)
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STEP 4: Write inverse function \(f^{-1}(x)\)
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📊 Graphical meaning
\(f\) (green) and \(f^{-1}\) (blue) are symmetric about \(y = x\) (red).

Adjust axis scale to explore reflection property.

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