Which function has an inverse that is also a function? a. {(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} b. {(–4, 6), (–2, 2), (–1, 6), (4, 2), (11, 2)} c. {(–4, 5), (–2, 9), (–1, 8), (4, 8), (11, 4)} d. {(–4, 4), (–2, –1), (–1, 0), (4, 1), (11, 1)}

Solution:

A relation is said to be a function if in different ordered pairs , each first element of ordered pair has different image And no two different elements of image have same preimage. For example {(5,2),(5,3)} is not a function.

We can find the inverse of an ordered pair by reversing the order of ordered pair.For example inverse of (x,y)→(y,x).If Both (x,y) and (y,x) are functions.

Option (B), (C), (D) are not true, ∵ In option (B) (2,-2), (2,4)→ Not a function

Option (C) (8,-1),(8,4)→→Not a function, Option(D) (1,4),(1,11)→→→Not a function.

Option A→{(–4, 3), (–2, 7), (–1, 0), (4, –3), (11, –7)} is a function.

∴ first element in each ordered pair has different image and when we reverse the order of element to get the inverse function, In that  inverse function, each first element of ordered pair has different image.