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Questions and Answers
What is the domain of the function f(x) = √(x + 1)?
What is the domain of the function f(x) = √(x + 1)?
What is the domain of the function f(x) = rac{1}{x-5}?
What is the domain of the function f(x) = rac{1}{x-5}?
What is the composition (g o f)(x) if f(x) = √(x - 1) and g(x) = 4x²?
What is the composition (g o f)(x) if f(x) = √(x - 1) and g(x) = 4x²?
What is the inverse function of f(x) = 3x - 6?
What is the inverse function of f(x) = 3x - 6?
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What is the domain of the function f(x) = √(4 - x²)?
What is the domain of the function f(x) = √(4 - x²)?
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Study Notes
Finding the Domain of a Function
- Determine the input values (x-values) for which the function is defined.
- Exclude values that result in division by zero or the square root of a negative number.
- The domain is the set of all possible input values.
Function Composition
- Substitute the expression of one function into another function.
- The composition of functions f(g(x)) involves plugging the expression of g(x) into f(x).
Finding the Inverse Function
- Switch the roles of x and y (input and output values).
- Solve for y (the inverse function).
- The inverse function reverses the original function's transformation of input values.
Verifying f(f⁻¹(x)) = x
- Substitute the inverse function into the original function.
- Simplify the expression to show it equals x.
- This confirms that the inverse function reverses the effects of the original function.
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Description
Test your understanding of functions in Algebra Class 10! This quiz covers finding the domain of a function, composing functions, and determining inverse functions. Additionally, you'll verify the relationship between a function and its inverse.
