IB Mathematics Applications & Interpretation Topic AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction Questionbank (HL)

IB Mathematics Applications & Interpretation Topic AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction Questionbank (HL) | RevisionDojo

Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 1

For a circle of radius $r$ , $A (r) = π r^{2}$ , $r \geq 0$ . Let $h (x) = x + 16 π$ .

Evaluate $A^{- 1} (81 π)$ .

[2]

Determine an expression for $(A^{- 1} \circ h) (x)$ .

[2]

Solve the equation $(A^{- 1} \circ h) (x) = 6$ .

[3]

Question 2

HLPaper 1

Consider the function $h (t) = 2 t^{3} + 1$ , defined on the domain $- 2 \leq t \leq 1$ .

Determine the range of $h (t)$ .

[2]

Find the inverse function $h^{- 1} (x)$ .

[2]

State the domain and range of $h^{- 1} (x)$ .

[2]

Question 3

HLPaper 1

The function $h$ is defined by $h (x) = (x + 1)^{3} - 2$ , $- 3 \leq x \leq 1$ .

Write down the range of $h$ .

[2]

Find an expression for $h^{- 1} (x)$ .

[2]

Write down the domain and range of $h^{- 1}$ .

[2]

Question 4

HLPaper 1

Consider the functions $p (x) = 1 + e^{- 2 x}$ and $q (x) = b x - 7$ , defined for $x \in R$ , where $b$ is a constant.

Determine an expression for $(q \circ p) (x)$ .

[2]

Given that $lim_{x \to \infty} (q \circ p) (x) = - 1$ , calculate the value of $b$ .

[4]

Question 5

HLPaper 2

A graphing package uses $r (x) = x^{2} + 9$ and $s (x) = x - 7$ .

Find $(r \circ s) (x)$ .

[2]

The graph of $(r \circ s) (x)$ is reflected in the $x$ -axis, then translated by the vector $(12 5)$ to give the graph of $h$ . Find the vertex of $h$ .

[3]

Show that $h (x) = - x^{2} + 24 x - 141$ .

[2]

The line $y = 6 x - 60$ is tangent to $h$ at the point $P$ . Find the $x$ -coordinate of $P$ .

[3]

The line $y = 6 x - 61$ intersects the graph of $h$ at two points. Find the coordinates of the two points of intersection.

[4]

IB Mathematics Applications & Interpretation AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction Questionbank

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IB Mathematics Applications & Interpretation AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 2.7—composite Functions, Finding Inverse Function Incl Domain Restriction Questionbank

Unlock all 26 questions with a free account