Question

which function is the inverse of (f(x) = 2x + 3)?

• (f^{-1}(x) = -\frac{1}{2}x - \frac{3}{2})
• (f^{-1}(x) = \frac{1}{2}x - \frac{3}{2})
• (f^{-1}(x) = -2x + 3)
• (f^{-1}(x) = 2x + 3)

Explanation:

Set up the equation

Using the Finding Inverses Algebraically knowledge point

$$ y = 2x + 3 $$

Swap variables

Using the Finding Inverses Algebraically knowledge point

$$ x = 2y + 3 $$

Solve for y

Using the Finding Inverses Algebraically knowledge point

$$
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$$

Express as inverse function

Using the Finding Inverses Algebraically knowledge point

$$ f^{-1}(x) = \frac{1}{2}x - \frac{3}{2} $$

Answer:

• (A) \(f^{-1}(x) = -\frac{1}{2}x - \frac{3}{2}\)
• (B) \(f^{-1}(x) = \frac{1}{2}x - \frac{3}{2}\) (Correct answer)
• (C) \(f^{-1}(x) = -2x + 3\)
• (D) \(f^{-1}(x) = 2x + 3\)