Relations and Functions Test

Result

Relations and Functions Test - 15

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Question 1
1 / -0

Let f :A → B, (for any two non-empty sets A and B),then f is invertible if

A
f is onto

B
f is many-one and onto

C
f is both one – one and onto

D
f is one – one

Solution

Any function is called invertible ,only when its inverse exists. The inverse of a function exists only when the function is bijective. i.e. both one –one and onto.
Question 2
1 / -0

If f = {(1, 4), (2, 5), (3, 6)} and g = {(4, 8), (5, 7), (6, 9)}, then gof is

A
{(1, 7), (2, 9), (3, 4) }

B
{(1, 7), (2, 4), (3, 9)}

C
{(1, 8), (2, 7), (3, 9)}

D
{(1, 7), (2, 8), (3, 9)}

Solution

(gof)(1) = g(f(1)) = g(4) = 8, (gof)(2) = g(f(2)) = g(5) = 7 and (gof)(3) = g(f(3)) = g(6) = 9.