Evaluating Composite Functions

What is the value of (f∘g)(x) if f(x) = x^2 and g(x) = x + 1?

• (x + 1)^2

• x^2 + 2x + 1

• x^2 + 1

• x^2 + 2

What is a composite function?

• A function that is formed by combining two functions, where the output of one function becomes the input of the other.

• A function that only takes one input and produces one output.

• A function that is defined only for positive integers.

• A function that cannot be expressed in terms of simpler functions.

If f(x) = x + 5 and g(x) = 2x, what is f(g(3))?

• 9

• 10

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• 12

How do you evaluate a composite function?

• First evaluate f(x) and then substitute that result into g.

• Evaluate g(x) and then substitute that result into f.

• Evaluate both f(x) and g(x) simultaneously.

• Evaluate f(x) and g(x) separately without substitution.

What is the output of g(f(-10)) if f(x) = 3x + 10 and g(x) = x - 2?

• -20

• -22

• -18

• None of these

If f(x) = 4x and g(x) = x/2, what is g(f(8))?

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• 14

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Given f(x) = x^2 and g(x) = 3x, find g(f(2)).

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• 14

What is the notation for composite functions?

• (f∘g)(x), which means f(g(x)).

• f(g(x)), which means (f∘g)(x).

• f∘g(x), which means g(f(x)).

• g(f(x)), which means (g∘f)(x).

What does the symbol '∘' represent in functions?

• The symbol '∘' represents the addition of two functions.

• The symbol '∘' represents the multiplication of two functions.

• The symbol '∘' represents the composition of two functions.

• The symbol '∘' represents the subtraction of two functions.

If f(x) = 2x + 3 and g(x) = x - 1, what is (f∘g)(2)?

• 3

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