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Questions and Answers
Determine the domain of definition of A = √ |x − 3| - 1
Determine the domain of definition of A = √ |x − 3| - 1
The domain is all real numbers x such that |x-3| ≥ 1, which means x ≤ 2 or x ≥ 4.
Determine the domain of definition of B = $\frac{2+x}{3+|-x|}$
Determine the domain of definition of B = $\frac{2+x}{3+|-x|}$
The domain is all real numbers.
Determine the domain of definition of C = $\frac{2}{-2+|x+5|}$
Determine the domain of definition of C = $\frac{2}{-2+|x+5|}$
x ≠ -7 and x ≠ -3
Determine the domain of definition of E = $\frac{x}{\sqrt{1-x+2}}$
Determine the domain of definition of E = $\frac{x}{\sqrt{1-x+2}}$
Solve in R: $-3-(x+1)^5 =29$
Solve in R: $-3-(x+1)^5 =29$
Solve in R: $|x − 1| - 2|x + 3| = 0$
Solve in R: $|x − 1| - 2|x + 3| = 0$
Solve in R: $(x - 3)^4 - 4 = 12$
Solve in R: $(x - 3)^4 - 4 = 12$
Solve in R: $\sqrt{3x-1} = -3$
Solve in R: $\sqrt{3x-1} = -3$
Solve in R: $|2x − 3| = (\sqrt{5} + 2)(2 - \sqrt{5})$
Solve in R: $|2x − 3| = (\sqrt{5} + 2)(2 - \sqrt{5})$
Solve in R: a- $|2 - x| ≥ 3$
Solve in R: a- $|2 - x| ≥ 3$
Deduce the domain of definition of g(x) = $\sqrt[3]{\frac{2-x-3}{x-9}}$
Deduce the domain of definition of g(x) = $\sqrt[3]{\frac{2-x-3}{x-9}}$
Simplify: A = $\sqrt{64} – 3\sqrt[4]{\frac{81}{16}} – 2\sqrt[3]{2^11} + 3\sqrt{16}$
Simplify: A = $\sqrt{64} – 3\sqrt[4]{\frac{81}{16}} – 2\sqrt[3]{2^11} + 3\sqrt{16}$
Simplify: B = $\sqrt[4]{(4-2\sqrt{3})^2} + \sqrt[6]{(5–4\sqrt{3})^3} - 2 \times \sqrt[4]{(1 - \sqrt{3})^4}$
Simplify: B = $\sqrt[4]{(4-2\sqrt{3})^2} + \sqrt[6]{(5–4\sqrt{3})^3} - 2 \times \sqrt[4]{(1 - \sqrt{3})^4}$
Simplify: D = $\sqrt{(x − 1)^2} + \sqrt[3]{8(x - y)^3} – \sqrt[4]{16(x - y)^4} + \sqrt[5]{(1-y)^5}$ knowing that x < 0 < y
Simplify: D = $\sqrt{(x − 1)^2} + \sqrt[3]{8(x - y)^3} – \sqrt[4]{16(x - y)^4} + \sqrt[5]{(1-y)^5}$ knowing that x < 0 < y
Simplify: E = $\frac{2^{-4} \times 2^8}{\sqrt[3]{\sqrt{2^2}}}$
Simplify: E = $\frac{2^{-4} \times 2^8}{\sqrt[3]{\sqrt{2^2}}}$
Simplify: F = $\frac{ n 10^{n+2} - 9 \times 10^{n+1}}{ 5^n \times 3 + (n+1) 5^n \times 7}$
Simplify: F = $\frac{ n 10^{n+2} - 9 \times 10^{n+1}}{ 5^n \times 3 + (n+1) 5^n \times 7}$
Given F = $\frac{16^{n + \frac{3}{2}} \times 4^{2n}}{2 \times 8^{2n} - 64^n}$, prove that F = $ \frac{1}{2^{2(n-1)}}$
Given F = $\frac{16^{n + \frac{3}{2}} \times 4^{2n}}{2 \times 8^{2n} - 64^n}$, prove that F = $ \frac{1}{2^{2(n-1)}}$
Given F = $\frac{16^{n + \frac{3}{2}} \times 4^{2n}}{2 \times 8^{2n} - 64^n}$, Calculate n if F = 256
Given F = $\frac{16^{n + \frac{3}{2}} \times 4^{2n}}{2 \times 8^{2n} - 64^n}$, Calculate n if F = 256
Find y in terms of x: $y^{\frac{1}{3}} = x^2$
Find y in terms of x: $y^{\frac{1}{3}} = x^2$
Find y in terms of x: $(y − 1)^2 = x^3$
Find y in terms of x: $(y − 1)^2 = x^3$
Given -2 < x < -1 and 1 < y < 2. Bound x + 3, then deduce the arrangement each of the following expressions in increasing order: (x + 3) ; (x + 3)² ; 1 ; $\frac{1}{x+3}$ ; $\sqrt{x+3}$
Given -2 < x < -1 and 1 < y < 2. Bound x + 3, then deduce the arrangement each of the following expressions in increasing order: (x + 3) ; (x + 3)² ; 1 ; $\frac{1}{x+3}$ ; $\sqrt{x+3}$
Given -2 < x < -1 and 1 < y < 2. Bound y - 1, then deduce the arrangement each of the following expressions in increasing order: $\sqrt{y-1}$ ; 1 ; (y - 1) ; (y − 1)² ; $\frac{1}{y-1}$
Given -2 < x < -1 and 1 < y < 2. Bound y - 1, then deduce the arrangement each of the following expressions in increasing order: $\sqrt{y-1}$ ; 1 ; (y - 1) ; (y − 1)² ; $\frac{1}{y-1}$
Study Notes
- The worksheet covers topics in math for class SE1 B.
Domain of Definition
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To determine the domain of definition, consider restrictions for each expression.
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If A = √ |x − 3| - 1, then |x-3| - 1 must be greater than or equal to zero.
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If B = (2+x) / (3+|-x|), then 3 + |-x| cannot equal zero.
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If C = 2 / (-2+|x+5|), then -2 + |x+5| cannot equal zero.
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If E = x / √1-x+2|, then 1 - x + 2 must be greater than zero.
Solving Equations in R
- Solve a series of equations in the set of real numbers (R)
- −3−(x + 1)⁵ = 29
- |x − 1| - 2|x + 3| = 0
- (x - 3)⁴ - 4 = 12
- √3x − 1 = -3
- |2x − 3| = (√5 + 2)(2 – √5)
- |2 - x| ≥ 3
Domain of a Function
- The domain of definition of g(x) = √(2-x-3)/(x-9) requires 2-x-3 ≥ 0, and x-9 > 0
Simplifying Expressions
- Simplify various algebraic expressions:
- A = √64 – 3∜81 – 2√2¹¹ + 3∜16
- B = ⁴√ (4-2√3)⁴ + ⁶√ (5–4√3)⁶ - 2x³√ (1 - √3)⁴
- D = √(x − 1)² + ³√8(x - y)³ – ⁴√16(x - y)⁴ + ⁵√ (1-y)⁵ given x < 0 < y
- E = (2⁻⁴ x 2⁸) / ³√(√2²)
- F = (n * 10ⁿ⁺² - 9 x 10ⁿ⁺¹) / (5ⁿ * 3 + 5ⁿ * 7)
Given Equation
- Given F = (16ⁿ⁺³ x 4²ⁿ) / (2 x 8²ⁿ - 64ⁿ) with two sub-problems
- Prove that: F = 1 / (2²⁽ⁿ⁻¹⁾)
- Calculate n if F = 256
Finding y in Terms of x
- y¹/³ = x²
- (y − 1)² = x²⁄³
Bounding Expressions and Ordering
- Given the condition of -2 < x < -1 and 1 < y < 2.
- Bound x + 3 and subsequently arrange these expressions in increasing order: (x + 3), (x + 3)², 1/(x+3), √x + 3
- Bound y - 1, and arrange these expressions in increasing order: √y−1, 1, (y - 1), (y − 1)², 1/(y−1)
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Description
Worksheet covering domains of definition by considering restrictions for square roots and fractions. Includes solving equations in the set of real numbers. Also involves simplifying algebraic expressions with radicals and exponents.
