DP Mathematics HL Questionbank

Description

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 $y = f\left( x \right)$...
• 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.
• 12M.1.hl.TZ2.11c: (i)     Find an expression for the inverse function ${f^{ - 1}}(x)$ . (ii)     State the...
• 12N.1.hl.TZ0.12c: Show that ${F_{ - n}}(x)$ is an expression for the inverse of ${F_n}$ .
• 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...
• 11M.1.hl.TZ2.8: A function is defined by...
• 09N.1.hl.TZ0.4: Consider the function f , where $f(x) = \arcsin (\ln x)$. (a)     Find the domain of f . (b)...
• SPNone.1.hl.TZ0.13c: Obtain expressions for the inverse function ${f^{ - 1}}$ and state their domains.
• 10M.1.hl.TZ2.10: A function f is defined by $f(x) = \frac{{2x - 3}}{{x - 1}},{\text{ }}x \ne 1$. (a)     Find...
• 10N.1.hl.TZ0.9: Consider the function $f:x \to \sqrt {\frac{\pi }{4} - \arccos x}$. (a)     Find the largest...
• 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;
• 09N.2.hl.TZ0.9: (a)     Given that the domain of $g$ is $x \geqslant a$ , find the least value of $a$ such...
• 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 ${f^{ - 1}}(x)$.
• 15N.2.hl.TZ0.12b: (i)     Explain why $f$ does not have an inverse. (ii)     The domain of $f$ is restricted...
• 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 ${f^{ - 1}}$.