Composition of Functions & Function Operations

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What is the composition of functions?

Back

The composition of functions is an operation that takes two functions, f and g, and produces a new function, denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

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How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the input value into the function's equation and simplify.

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CCSS.HSF.IF.A.2

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What is the difference between f(x) and g(x) when f(x) = x^2 + 9 and g(x) = x - 9?

Back

The difference f(x) - g(x) is calculated by subtracting g(x) from f(x), resulting in x^2 - x + 18.

Tags

CCSS.HSF-BF.A.1B

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What does g(5) represent in function notation?

Back

g(5) represents the output of the function g when the input is 5.

Tags

CCSS.HSF.IF.A.2

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How do you evaluate g(4x)?

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To evaluate g(4x), substitute 4x into the function g and simplify the expression.

Tags

CCSS.HSF.IF.A.2

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What is the significance of function operations in mathematics?

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Function operations, such as addition, subtraction, multiplication, and composition, allow us to combine and manipulate functions to solve complex problems.

Tags

CCSS.HSF-BF.A.1B

Front

What is the output of f[g(5)] if f(x) = 2x + 2 and g(5) = 375?

Back

To find f[g(5)], substitute g(5) into f: f(375) = 2(375) + 2 = 752.

Tags

CCSS.HSF-BF.A.1C

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How do you find the sum of two functions, f and g?

Back

The sum of two functions is found by adding their outputs: (f + g)(x) = f(x) + g(x).

Tags

CCSS.HSF-BF.A.1B

Front

What is the formula for the difference of two functions?

Back

The difference of two functions is given by (f - g)(x) = f(x) - g(x).

Tags

CCSS.HSF-BF.A.1B

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What is the product of two functions?

Back

The product of two functions is defined as (f * g)(x) = f(x) * g(x).

Tags

CCSS.HSF-BF.A.1B