Exploring Functions and Mappings

What are the different types of mappings?

• Many-to-Few

• One-to-One, One-to-Many, Many-to-One, Many-to-Many, Functional Mapping

• One-to-Two

• Two-to-Many

Identify the type of mapping for the function f(x) = 3x + 2.

• Linear mapping

• Exponential mapping

• Quadratic mapping

• Cubic mapping

Perform the composite function (f ∘ g)(x) if f(x) = x^2 and g(x) = 2x + 1.

• 2x^2 + 2x + 1

• x^2 + 2x + 1

• 4x^2 + 1

• 4x^2 + 4x + 1

Find the inverse function of f(x) = 2x - 5.

• f^(-1)(x) = (x + 5) / 2

• f^(-1)(x) = 2x + 5

• f^(-1)(x) = x - 5

• f^(-1)(x) = 2(x - 5)

Calculate the domain of the function f(x) = 1/(x - 3).

• x < 3 or x > 3

• x = 3 only

• All real numbers except x = 3

• All real numbers

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

• (-∞, 0)

• [1, 2]

• [0, ∞)

• (0, 1)

Determine the composite function (g ∘ f)(x) for g(x) = x + 4 and f(x) = 3x.

• 9x + 4

• x + 3

• 3x + 4

• 3x - 4

Find the inverse of the function f(x) = (x + 1)/2.

• f^(-1)(x) = 2x - 1

• f^(-1)(x) = x - 1

• f^(-1)(x) = 2/x

• f^(-1)(x) = x + 1

What is the domain of the function f(x) = √(x - 4)?

• [0, 4)

• (4, 5)

• [4, ∞)

• (−∞, 4)

Calculate the range of the function f(x) = -x^2 + 6.

• (-∞, 6]

• (6, ∞)

• (0, 6)

• (-∞, 0)