Exploring Inverse Relations

Define inverse relations in your own words.

• Inverse relations are obtained by reversing the order of the pairs in a relation.

• Inverse relations involve adding pairs to a relation.

• Inverse relations are only applicable to functions.

• Inverse relations are the same as direct relations.

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

• f^(-1)(x) = (x - 3) / 2

• f^(-1)(x) = 2x - 3

• f^(-1)(x) = x + 3

• f^(-1)(x) = 2(x + 3)

How can you identify if two functions are inverses of each other?

• Two functions are inverses if f(x) + g(x) = 0.

• Two functions are inverses if their graphs are parallel.

• Two functions are inverses if f(g(x)) = x and g(f(x)) = x.

• Two functions are inverses if f(g(x)) = g(f(x)).

Graph the function f(x) = x^2 and its inverse.

• The graph of f(x) = x^2 is a straight line.

• The inverse of f(x) = x^2 is y = -sqrt(x) for all x.

• The graph of f(x) = x^2 is a parabola opening upwards, and its inverse is the curve y = sqrt(x) for x >= 0.

• The graph of f(x) = x^2 is a circle centered at the origin.

Evaluate the inverse function f^-1(x) if f(x) = 3x - 5.

• f^-1(x) = (x + 5) / 3

• f^-1(x) = (x - 5) / 3

• f^-1(x) = 3x + 5

• f^-1(x) = 3(x + 5)

What is the domain of the function f(x) = sqrt(x)?

• (0, ∞)

• (-∞, 0)

• [0, ∞)

• [-1, 1]

Determine the range of the function f(x) = 1/x.

• (0, +∞)

• [0, +∞)

• (-∞, +∞)

• (-∞, 0) ∪ (0, +∞)

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

• f^-1(x) = 4 - x

• f^-1(x) = x - 4

• f^-1(x) = x + 4

• f^-1(x) = x / 4

Explain how to find the inverse of a function algebraically.

• The inverse can be determined by taking the derivative of the function.

• The inverse is found by multiplying the variables and simplifying the equation.

• To find the inverse, you must graph the function and reflect it over the line y=x.

• The inverse of a function is found by swapping the variables and solving for the new dependent variable.

Graph the inverse of the function f(x) = x^3.

• The graph of the inverse function is y = x^3 + 1.

• The graph of the inverse function is y = 3x.

• The graph of the inverse function is y = x^(1/3).

• The graph of the inverse function is y = x^2.