Podcast
Questions and Answers
Simplify the expression: (\sqrt[3]{8} \cdot \sqrt[3]{9})
Simplify the expression: (\sqrt[3]{8} \cdot \sqrt[3]{9})
(\sqrt[3]{72})
Solve the equation: ((x + 3)^3 = 14)
Solve the equation: ((x + 3)^3 = 14)
x \approx -1.15
Write the expression in simplest form: (\sqrt[3]{x^2} \cdot \sqrt[3]{x^4})
Write the expression in simplest form: (\sqrt[3]{x^2} \cdot \sqrt[3]{x^4})
(x^2)
Simplify the expression: (\frac{x^3y}{81x^5y^3})
Simplify the expression: (\frac{x^3y}{81x^5y^3})
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Given the functions (f(x) = 5x^2 - x^3) and (g(x) = 4x^3), find (f(x) - g(x))
Given the functions (f(x) = 5x^2 - x^3) and (g(x) = 4x^3), find (f(x) - g(x))
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Given (f(x) = 4x - 1) and (g(x) = x - 6), find (f(g(x)))
Given (f(x) = 4x - 1) and (g(x) = x - 6), find (f(g(x)))
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Verify that (f(x) = 3x - 2) and (g(x) = \frac{x + 2}{3}) are inverse functions.
Verify that (f(x) = 3x - 2) and (g(x) = \frac{x + 2}{3}) are inverse functions.
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Find the inverse function, (f^{-1}(x)), of (f(x) = 2x + 7)
Find the inverse function, (f^{-1}(x)), of (f(x) = 2x + 7)
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Flashcards
Radical form
Radical form
A mathematical expression that involves roots, such as square or cube roots.
Evaluate the expression
Evaluate the expression
To calculate the value of an expression by simplifying it.
Solving equations
Solving equations
Finding the value of variables that satisfy the equation.
Simplification of expressions
Simplification of expressions
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Inverse functions
Inverse functions
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Sum of functions
Sum of functions
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Difference of functions
Difference of functions
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Product of functions
Product of functions
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Study Notes
Unit 7 Quiz - 7.1-7.4
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Rewrite expressions in radical form and evaluate: Example problems involve rewriting expressions like 1.16⁴, 2.25⁻², -3⁻³²⁵, and (-8)⁴ in radical form and then calculating their values.
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Solve equations and round to two decimal places: Solve equations like 5. 2x² = 12 and 6. (x + 3)³ = 14, rounding the solutions to two decimal places.
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Simplify expressions: Simplify expressions involving radicals and exponents, such as √3 - √9, ∛x²√x, (x)³⁻⁴, √81x⁵y³, (x³ y / x⁻²y⁴), 8⁻³/⁵, 3⁵/⁹, and 2³ + ⅓(2³).
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Simplify expressions with variables (positive variables): Simplify expressions that involve variables and assume that all variables are positive, such as 11. √x². √x.
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Perform indicated operations with functions: Given f(x) = 5x² - x and g(x) = 4x³, find f(x) - g(x) and f(x) * g(x).
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Perform indicated operations with functions (with 4x⁻¹ and x-6): Given f(x)=4x⁻¹ and g(x)=x−6, find f(g(x)), g(f(x)), f(x)+g(x), f(x)/g(x), f(f(x)).
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Verify inverse functions: Verify if f(x) and g(x) are inverse functions, specifically f(x) = 3x - 2 and g(x) = (x+2)/3.
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Find the inverse function: Find the inverse functions of f(x) = 2x + 7 and g(x) = 3x⁴, ensuring x > 0.
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Description
This quiz covers key concepts from Unit 7, focusing on rewriting expressions in radical form, solving equations, and simplifying expressions involving exponents and radicals. Students will also perform operations with functions and work with positive variable expressions. Test your understanding and skills with these essential functions and radical expressions.
