Exploring Inverse Functions: Domain, Range, and Graphs

How do you find the domain of a square root function?

• There is no need to find the domain; it's always all real numbers.

• Set the expression under the square root to be greater than or equal to zero.

• Set the expression under the square root to be less than zero.

• Set the expression under the square root to be equal to zero.

What is the inverse function of f(x) = (2x + 5) / (3x - 1)?

• y = (3x + 5) / (2 - x)

• y = (x + 5) / (3x - 2)

• y = (3x + 5) / (2x - 1)

• y = (3x + 5) / (3x - 2)

For a square root function, what is the lowest value the function can take?

• 1

• -1

• 0

• It can take any real number value.

What is the inverse function of f(x) = 3x - 8?

• y = 3x + 8

• y = (3x - 8)^-1

• y = (x - 8) / 3

• y = (x + 8) / 3

What is the relationship between the domain of a function and the range of its inverse?

• They are exactly the same.

• There is no relationship.

• The domain of the function becomes the range of its inverse.

• The range of the function becomes the domain of its inverse.

How can you prove two functions are inverses of each other?

• By showing they have the same domain and range.

• By graphing them.

• By solving them for y.

• By finding the composite function f(g(x)) and g(f(x)) and showing both equal x.

What does the vertical line test determine?

• If a graph represents a function.

• If a function is continuous.

• If a function is differentiable.

• If a function has an inverse.

What does the horizontal line test determine?

• If a function is differentiable.

• If a function has an inverse that is also a function.

• If a function is continuous.

• If a graph represents a function.

If a function passes the horizontal line test, what does it imply?

• The function is not one-to-one.

• The function does not have an inverse.

• The function has an inverse that is also a function.

• The function is discontinuous.

What is the inverse function of f(x) = e^(3x+1) - 5?

• y = ln(x+5) - 1/3

• y = ln(x-5)/3 + 1/3

• y = 3ln(x+5) - 1

• y = ln(x+5)/3 - 1/3