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...