Understanding Domains of Functions

The video tutorial explores the concept of finding the domain of functions, using examples of g(x) and h(x). It explains the conditions under which these functions are defined, focusing on avoiding division by zero and ensuring non-negative values under radicals. The tutorial also discusses the implications of simplifying function expressions and how it affects the domain. The video concludes with a detailed analysis of the domain of h(x), considering its composite definition and potential simplification issues.

What is the function g(x) defined as?

• 1 over the square root of 6 minus the absolute value of x

• 1 over the square root of x

• 1 over the square root of 6 minus x

• 1 over the square root of x minus 6

When is the function g(x) not defined?

• When the denominator is zero or negative

• When x is greater than 6

• When x is positive

• When x is negative

What is the domain of g(x) in set notation?

• x is a member of real numbers such that x is not equal to 6

• x is a member of real numbers such that -6 < x < 6

• x is a member of real numbers such that x is less than 6

• x is a member of real numbers such that x is greater than 6

What is the composite definition of h(x) when x is not equal to 5?

• x plus 10 over x plus 10 times x minus 9 times x minus 5 times x minus 5

• x plus 10 over x plus 10 times x minus 5

• x plus 10 over x minus 9

• x plus 10 over x minus 5

What value does h(x) take when x equals 5?

• 0

• 10

• Undefined

• Pi

What causes h(x) to be undefined?

• When x equals 5

• When x equals 9 or -10

• When x is greater than 9

• When x is less than -10

Why can't we simplify h(x) by canceling x + 10?

• It would make the function equal to zero

• It would not affect the function

• It would create a different function definition

• It would make the function undefined

What is the domain of h(x) in set notation?

• x is a member of real numbers such that x is not equal to 9 and -10

• x is a member of real numbers such that x is less than -10

• x is a member of real numbers such that x is greater than 9

• x is a member of real numbers such that x is not equal to 5

What happens if x equals 9 in the function h(x)?

• The function is defined

• The function equals pi

• The function is undefined due to division by zero

• The function equals zero

What happens if x equals -10 in the function h(x)?

• The function is defined

• The function equals pi

• The function is undefined due to division by zero

• The function equals zero