Podcast
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 ; $\frac{1}{y-1}$
Flashcards are hidden until you start studying
Study Notes
- The worksheet covers topics in math for class SE1 B.
Domain of Definition
-
To determine the domain of definition, consider restrictions for each expression.
-
If A = √ |x − 3| - 1, then |x-3| - 1 must be greater than or equal to zero.
-
If B = (2+x) / (3+|-x|), then 3 + |-x| cannot equal zero.
-
If C = 2 / (-2+|x+5|), then -2 + |x+5| cannot equal zero.
-
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)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
