Find the domain and range of two functions dividing and composition

What is the main concept to understand when performing addition, subtraction, or multiplication on functions?

• The intersection of the domains

• The range of the functions

• The difference of the domains

• The sum of the domains

When dividing two functions, what new restriction is introduced?

• The range must be finite

• The functions must be polynomials

• The denominator cannot be zero

• The numerator must be positive

How does introducing a radical in a function affect its domain?

• It requires the domain to be all real numbers

• It has no effect on the domain

• It removes all restrictions

• It adds a restriction to only positive numbers

In function composition, what happens to the domain of the input function?

• It is reduced

• It is preserved

• It is expanded

• It is ignored

Why is it important to consider domain restrictions before simplifying a composition of functions?

• To increase the domain

• To simplify the calculation

• To avoid undefined values

• To ensure the range is correct

What is the domain of the composition G(F(x)) if F(x) = x^2 and G(x) = sqrt(x)?

• All real numbers

• Negative numbers only

• Positive numbers only

• Zero to infinity

How does the order of functions in a composition affect the domain?

• It does not affect the domain

• It changes the function type

• It determines the range

• It affects which domain restrictions are applied

What must be considered when finding the domain of a composition of functions?

• Only the domain of the input function

• Both the input function and the composition

• Neither function's domain

• Only the domain of the output function

If F(x) = sqrt(x) and G(x) = x^2, what is the domain of F(G(x))?

• All real numbers

• Negative infinity to zero

• Negative numbers only

• Zero to infinity

Why can't you plug negative numbers into the function sqrt(x)?

• Because it is not continuous

• Because it is not a polynomial

• Because it is undefined

• Because it results in a complex number