Inverting a Restricted Absolute Value Function

00:00 4 marks

  • Exam Style - Paper 2
  • SL & HL
  • Tier 2
  • Piecewise functions
  • Inverse Functions
  • Absolute value properties

Given the function \( f(x) = |2x-3| \) with the domain restricted to \( x \geq 1.5 \), find the inverse function \( f^{-1}(y) \) and state its domain.

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Hint

Examine the effect of the domain restriction which allows the absolute value to be removed, then solve for \( x \) in terms of \( y \).

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Complete Answer

\( f^{-1}(y) = \frac{y+3}{2} \) for \( y \geq 0 \)

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