Exploring Functions: Domain, Range, Composite, and Inverse

What does the notation f(x) represent?

• The input variable

• The output variable

• The domain of the function

• The function itself

If f(x) = x^2 - 2, what is f(3)?

• 9

• 11

• 7

• 5

What is the domain of the function f(x) = x^2 - 2?

• All integers

• All negative numbers

• All positive numbers

• All real numbers

For the function g(x) = x + 3, what is the range?

• All negative numbers

• All real numbers

• All positive numbers

• All integers

What is the domain of the function h(x) = √(x + 1)?

• x ≥ -1

• x > -1

• x < -1

• x ≤ -1

What does the composite function f(g(x)) represent?

• The function f(x) applied to g(x)

• The sum of f(x) and g(x)

• The product of f(x) and g(x)

• The function g(x) applied to f(x)

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

• (x + 3)^2 - 2

• x^2 - 2 + 3

• x^2 + 3 - 2

• x^2 + 1

What is the first step in finding the inverse of a function?

• Multiply by a constant

• Add a constant

• Swap x and y

• Square both sides

What is the inverse of the function f(x) = x^2 - 2?

• x^2 - 2

• x^2 + 2

• √(x + 2)

• √(x - 2)

What is the inverse of the function h(x) = √(x + 1)?

• x^2 + 1

• x^2 - 1

• √(x - 1)

• √(x + 1)