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AP Calculus AB Unit 1A3: Function Composition and Inverses — practice questions — page 2

Explore 95 free Unit 1A3: Function Composition and Inverses questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A3: Function Composition and Inverses questions and exercises with answers

Showing questions 31–60 of 95.

If cot x = -5/12 and x lies in the SECOND quadrant, then sin x equals:Read the answer and worked solution →In which quadrant is tan x POSITIVE while sin x is NEGATIVE?Read the answer and worked solution →The DOMAIN of y = tan x is:Read the answer and worked solution →sin(2nπ + x) equals (for any integer n):Read the answer and worked solution →The RANGE of y = sec x is:Read the answer and worked solution →At which of the following x-values is cos x equal to zero?Read the answer and worked solution →The value of cos(-π/3) is:Read the answer and worked solution →6 radians converts to approximately:Read the answer and worked solution →If the sum of the first $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?Read the answer and worked solution →$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) = $Read the answer and worked solution →$\sin^{-1}\left(\sin\tfrac{2\pi}{3}\right)$ equalsRead the answer and worked solution →$\cot^{-1}\left(-\tfrac{1}{\sqrt{3}}\right) = $Read the answer and worked solution →For $x = -2$, the value of $\tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$ equalsRead the answer and worked solution →The domain of the function $f(x) = \sin^{-1}(x)$ isRead the answer and worked solution →For every $x \in [-1, 1]$, the value of $\sin^{-1}(x) + \cos^{-1}(x)$ isRead the answer and worked solution →$\cos^{-1}\left(\cos\tfrac{7\pi}{6}\right)$ equalsRead the answer and worked solution →The principal value of $\tan^{-1}(1)$ isRead the answer and worked solution →The range of $\cos^{-1}(x)$ isRead the answer and worked solution →$\displaystyle \sum_{n=1}^{\infty} \tan^{-1}\left(\frac{1}{n^2 + n + 1}\right)$ equalsRead the answer and worked solution →All real $x$ satisfying $\sin^{-1}(x) + \sin^{-1}(1-x) = \cos^{-1}(x)$ areRead the answer and worked solution →$\tan^{-1}\left(\tfrac{1}{2}\right) + \tan^{-1}\left(\tfrac{1}{3}\right)$ equalsRead the answer and worked solution →Which of the following is a linear equation in one variable?Read the answer and worked solution →Solve for t: 5t − 3 = 3t − 5Read the answer and worked solution →Solve for y: 2y + 5/3 = 26/3 − yRead the answer and worked solution →The MAXIMUM possible measure of an exterior angle of a regular polygon is:Read the answer and worked solution →Which of the following is a perfect cube?Read the answer and worked solution →How many perfect cubes are there from 1 to 1000 (both included)?Read the answer and worked solution →What is the cube of 12?Read the answer and worked solution →Which of the following numbers is NOT a perfect cube?Read the answer and worked solution →The units (one's) digit of (78)³ is:Read the answer and worked solution →

Worked practice questions

If cot x = -5/12 and x lies in the SECOND quadrant, then sin x equals:

  1. -5/13
  2. 12/13
  3. 5/13
  4. -12/13
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Correct answer: B. 12/13

cot x = cos x / sin x = -5/12. Using 1 + cot²x = cosec²x: cosec²x = 1 + 25/144 = 169/144 → cosec x = ±13/12. In Quadrant II, sin x > 0 so cosec x > 0 We have → cosec x = 13/12 → sin. So x = 12/13.

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In which quadrant is tan x POSITIVE while sin x is NEGATIVE?

  1. I
  2. III
  3. II
  4. IV
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Correct answer: B. III

**Quadrant signs:** I (all +), II (sin/cosec +), III (tan/cot +), IV (cos/sec +). Quadrant III has both sin and cos negative → sin x < 0 and tan x = sin/cos > 0.

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The DOMAIN of y = tan x is:

  1. {x ∈ ℝ : -1 ≤ x ≤ 1}
  2. All real numbers
  3. {x ∈ ℝ : x ≠ (2n+1)π/2, n ∈ ℤ}
  4. {x ∈ ℝ : x ≠ nπ, n ∈ ℤ}
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Correct answer: C. {x ∈ ℝ : x ≠ (2n+1)π/2, n ∈ ℤ}

tan x = sin x / cos x is undefined where cos x = 0, i.e. at x = (2n+1)π/2. Hence domain = ℝ \ {(2n+1)π/2 : n ∈ ℤ}. Range of tan x is all of ℝ.

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More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A1: Relations, Functions and GraphsUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits