Composition of Function with Domain

The video tutorial covers the composition of functions and how to determine their domains. It provides multiple examples, including G of F of X, H of F of X, J of H of X, and F of F of X, illustrating how to solve these compositions and analyze domain restrictions. The tutorial emphasizes understanding the domain of the input function and the resulting composition to identify any new restrictions.

What is the domain of a linear function?

• Zero to positive infinity

• Only negative values

• Only positive values

• Negative infinity to positive infinity

When composing G(F(x)), what is the resulting function's domain if both G(x) and F(x) are defined for all values?

• Only positive values

• Negative infinity to zero

• Zero to positive infinity

• Negative infinity to positive infinity

What is the domain of a quadratic function when composed with another function?

• Negative infinity to positive infinity

• Only negative values

• Zero to positive infinity

• Only positive values

In the composition H(F(x)), what must be true about the expression under the radical?

• It must be a positive integer

• It must be equal to zero

• It must be greater than or equal to zero

• It must be less than zero

What happens to the domain when a function is placed under a radical?

• The domain is limited to negative integers

• The domain becomes unrestricted

• The domain is limited to values that make the expression under the radical non-negative

• The domain is limited to positive integers

How does placing a function under a radical affect its domain?

• It has no effect on the domain

• It expands the domain to include all real numbers

• It restricts the domain to values that make the expression under the radical non-negative

• It restricts the domain to positive values only

What is the domain of the function J(F(x)) if the denominator cannot be zero?

• All values except those that make the denominator zero

• All real numbers

• Only positive values

• Only negative values

What must be checked when composing functions with rational expressions?

• The denominator must not be zero

• The expression must be a linear function

• The expression must be a perfect square

• The numerator must be zero

In the composition F(F(x)), what is the domain if F(x) is defined for all values?

• Zero to positive infinity

• Negative infinity to positive infinity

• Only negative values

• Only positive values

What is a key consideration when determining the domain of a composed function?

• The coefficients of the function

• The degree of the polynomial

• The restrictions of the function being plugged into

• The range of the input function