Exploring Inverse Functions

What is the inverse of the function f(x) = 2x + 3?

• f^(-1)(x) = 2(x + 3)

• f^(-1)(x) = x / 2 + 3

• f^(-1)(x) = (x - 3) / 2

• f^(-1)(x) = 2x - 3

Given the table of values for f(x): (1, 5), (2, 7), (3, 9), what are the corresponding values for f^-1(x)?

• (7, 3)

• (9, 1)

• (5, 1), (7, 2), (9, 3)

• (5, 2)

Graph the function f(x) = x^2 for x ≥ 0 and its inverse. What is the shape of the graph?

• The graph is a parabola opening downwards and a horizontal line.

• The graph is a straight line with a negative slope.

• The graph consists of a circle centered at the origin.

• The graph consists of a parabola opening upwards and its reflection, which is a curve increasing from the origin.

How can you verify that two functions are inverses of each other?

• Ensure that f(g(x)) = g(f(x)) for all x.

• Verify that f(x) = g(x) for all x.

• Check if f(g(x)) = x and g(f(x)) = x.

• Check if f(x) + g(x) = 0 and g(x) + f(x) = 0.

If f(x) = 3x - 4, what is f^-1(x)?

• 3(x - 4)

• (x + 4)/3

• (x - 4)/3

• (3x + 4)

Using the table of values, determine if the function is one-to-one: (1, 2), (2, 3), (3, 4), (4, 5).

• No, the function is not one-to-one.

• Yes, the function is one-to-one.

• The function is one-to-many.

• The function has repeated values.

What is the graphical relationship between a function and its inverse?

• The function and its inverse are parallel to the x-axis.

• The function and its inverse are reflections across the line y = x.

• The function and its inverse intersect at the origin.

• The function and its inverse are identical functions.

If f(x) = x + 5, what is the domain of f^-1(x)?

• x > 5

• All real numbers

• x = 0

• x < -5

Analyze the behavior of the function f(x) = 1/x. What is its inverse?

• f^(-1)(x) = 1/x

• f^(-1)(x) = x

• f^(-1)(x) = x^2

• f^(-1)(x) = -1/x

Given the function f(x) = x^3, what is the inverse function and how do you graph it?

• f^(-1)(x) = 1/x

• The inverse function is f^(-1)(x) = x^(1/3).

• f^(-1)(x) = 3x^2

• f^(-1)(x) = x^2