DP Mathematics HL Questionbank

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Directly related questions

• 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 \(y = f\left( x \right)\)...
• 16N.2.hl.TZ0.2: Find the acute angle between the planes with equations \(x + y + z = 3\) and \(2x - z = 2\).
• 17N.1.hl.TZ0.11a: Determine whether \({f_n}\) is an odd or even function, justifying your answer.
• 12M.1.hl.TZ2.11b: Find an expression for the composite function \(f \circ g(x)\) in the form...
• 12N.1.hl.TZ0.12a: Find an expression for \((f \circ f)(x)\) .  
• 08M.1.hl.TZ1.8: The functions f and g are defined as: \[f(x) = {{\text{e}}^{{x^2}}},{\text{ }}x \geqslant...
• 08M.1.hl.TZ2.4: Let \(f(x) = \frac{4}{{x + 2}},{\text{ }}x \ne - 2{\text{ and }}g(x) = x - 1\). If...
• 13M.2.hl.TZ1.13d: (i)     With f and g as defined in parts (a) and (b), solve \(g \circ f(x) = 2\). (ii)     Let...
• 10M.1.hl.TZ1.2: Shown below are the graphs of \(y = f(x)\) and \(y = g(x)\).     If \((f \circ g)(x) = 3\),...
• 14M.2.hl.TZ1.12: Let \(f(x) = \left| x \right| - 1\). (a)     The graph of \(y = g(x)\) is drawn below.      ...
• 14M.1.hl.TZ2.14b: Find an expression for the composite function \(h \circ g(x)\) and state its domain.
• 15M.1.hl.TZ1.9a: Show that \(g \circ f(x) = 3\sin \left( {2x + \frac{\pi }{5}} \right) + 4\).
• 15M.1.hl.TZ1.9c: Given that \(g \circ f\left( {\frac{{3\pi }}{{20}}} \right) = 7\), find the next value of \(x\),...
• 15M.1.hl.TZ1.9b: Find the range of \(g \circ f\).
• 15M.1.hl.TZ2.11b: Hence show that \(g \circ f(x) = \frac{{\sin x + \cos x}}{{\sin x - \cos x}}\).
• 15M.1.hl.TZ2.11a: Find an expression for \(g \circ f(x)\), stating its domain.
• 15N.2.hl.TZ0.12a: The functions \(u\) and \(v\) are defined as \(u(x) = x - 3,{\text{ }}v(x) = 2x\) where...