Question

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)}

Answer 1

Answer:

(i)A function has inverse if it is one-one and on-to.

f={(1,10),(2,10),(3,10),(4,10)}

Since all elements have image 10, they do not have unique image.

∴ f is not one-one.

Since, f is not one-one,it do not have an inverse.

(ii)g={(5,4),(6,3),(7,4),(8,2)}

Since,5 and 7 have same image 4,g is not one-one.

Since g is not one-one,it does not have on inverse.

(iii)h={(2,7),(3,9),(4,11),(5,13)}

Since each element has a unique image h is one-one.

since,for every element,there is a corresponding element, ∴ his onto

Since function is both one--one and onto,it will have inverse

h={(2,7),(3,9),(4,11),(5,13)}

h

−1

={(7,2),(9,3),(11,4),(13,5)}

solution