Exploring Inverse Relations

Define inverse relations in your own words.

• Inverse relations involve adding new pairs to a relation.

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

• Inverse relations are the same as direct relations.

• Inverse relations are only applicable to numerical data.

What is the inverse of the relation {(1, 2), (3, 4)}?

• {(4, 1), (3, 2)}

• {(2, 4), (1, 3)}

• {(1, 3), (2, 4)}

• {(2, 1), (4, 3)}

Identify the inverse pair for the function f(x) = 2x + 3.

• f^(-1)(x) = x / 2 + 3

• f^(-1)(x) = (x - 3) / 2

• f^(-1)(x) = 2x - 3

• f^(-1)(x) = 2(x + 3)

Graph the inverse of the function y = x^2 for x ≥ 0.

• y = -√x for x ≥ 0

• y = 1/x for x > 0

• y = x for x ≥ 0

• The inverse function is y = √x for x ≥ 0.

Evaluate the inverse function of f(x) = 3x - 5 at x = 4.

• 5

• 2

• 3

• 1

If f(a) = b, what is the relationship between a and b in terms of inverse relations?

• b is the input value for the function f.

• a is the pre-image of b under the function f.

• a and b are unrelated in the context of f.

• b is the image of a under the function f.

Determine if the pairs (2, 3) and (3, 2) are inverse pairs.

• No, (2, 3) and (3, 2) are not inverse pairs.

• (3, 2) is the inverse of (2, 3).

• (2, 3) is the inverse of (3, 2).

• Yes, (2, 3) and (3, 2) are inverse pairs.

How do you graph the inverse of a linear function?

• Graph the inverse by reflecting the original graph over the x-axis.

• Graph the inverse by swapping x and y in the original equation and plotting the resulting function.

• To find the inverse, multiply the original function by -1.

• Graph the inverse by adding a constant to the original function.

What is the inverse of the relation {(a, b), (b, c)}?

• {(b, c), (a, c)}

• {(a, c), (b, a)}

• {(a, b), (c, b)}

• {(b, a), (c, b)}

Evaluate f^-1(7) if f(x) = 2x + 1.

• 4

• 6

• 3

• 5