DP Mathematics HL Questionbank
Inverse function \({f^{ - 1}}\), including domain restriction. Self-inverse functions.
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- 18M.1.hl.TZ2.10c: The function \(h\) is defined by \(h\left( x \right) = \sqrt x \), for \(x\) ≥ 0. State the...
- 18M.1.hl.TZ2.10a: Find the inverse function \({f^{ - 1}}\), stating its domain.
- 18M.2.hl.TZ2.10a.iv: Explain why \(f\) is not a function for...
- 18M.2.hl.TZ2.10a.iii: Explain why \(f\) has no inverse on the given domain.
- 18M.2.hl.TZ2.10a.ii: With reference to your graph, explain why \(f\) is a function on the given domain.
- 18M.2.hl.TZ2.10a.i: Sketch the graph of \(y = f\left( x \right)\)...
- 16M.2.hl.TZ2.5: The function \(f\) is defined as...
- 16M.2.hl.TZ1.11d.ii: Solve \(({f^{ - 1}} \circ g)(x) < 1\).
- 16M.2.hl.TZ1.11d.i: Find an expression for \({g^{ - 1}}(x)\), stating the domain.
- 16M.2.hl.TZ1.11c.iii: Solve \({f^{ - 1}}(x) = 1\).
- 16M.2.hl.TZ1.11c.ii: For this value of a sketch the graphs of \(y = f(x)\) and \(y = {f^{ - 1}}(x)\) on the same set...
- 16M.2.hl.TZ1.11c.i: Write down the largest value of \(a\) for which \(f\) has an inverse. Give your answer correct to...
- 16N.2.hl.TZ0.10e: Find an expression for \({f^{ - 1}}(x)\).
- 16N.2.hl.TZ0.10d: Use your answers from parts (b) and (c) to justify that \(f\) has an inverse and state its domain.
- 17N.1.hl.TZ0.11a: Determine whether \({f_n}\) is an odd or even function, justifying your answer.
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- 13M.1.hl.TZ2.12d: (i) Find an expression for \({f^{ - 1}}(x)\). (ii) Sketch the graph of \(y = f(x)\),...
- 11N.1.hl.TZ0.9c: Explain why f has no inverse.
- 11N.2.hl.TZ0.8a: find \({f^{ - 1}}(x)\), stating its domain;
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- 14M.2.hl.TZ2.7b: Find the inverse function \({f^{ - 1}}\), stating its domain.
- 15M.1.hl.TZ1.6a: Find an expression for \({f^{ - 1}}(x)\).
- 15M.1.hl.TZ2.10c: Find all values of \(x\) for which \(f(x) = {f^{ - 1}}(x)\).
- 15M.1.hl.TZ2.10b: Find an expression for \({f^{ - 1}}(x)\).
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- 15N.2.hl.TZ0.12c: Consider the function defined by \(h(x) = \frac{{2x - 5}}{{x + d}}\), \(x \ne - d\) and...
- 14N.1.hl.TZ0.11a: (i) Find \({f^{ - 1}}(x)\). (ii) State the domain of \({f^{ - 1}}\).
