Question

please solve this question ​

Answer 1

Answer:

Given:

f : { 2,4,5 } —> { 2,3,6 }

f = { (2,3) , (4,6) , (5,2) }

g : { 2,3,6 } —> { 2,4 }

g = { (2,4) , (3,4) , (6,2) }

To find:

gof = ?

Solution:

It is given that;

f = { (2,3) , (4,6) , (5,2) }

ie;

f(2) = 3 --------(1)

f(4) = 6 --------(2)

f(5) = 2 --------(3)

Also,

g = { (2,4) , (3,4) , (6,2) }

ie;

g(2) = 4 --------(4)

g(3) = 4 --------(5)

g(6) = 2 --------(6)

Note:

If f : { 2,4,5 } —> { 2,3,6 } and

g : { 2,3,6 } —> { 2,4 } then gof will be a function defined from f to g ,ie;

gof : { 2,4,5 } —> { 2,4 }.

Here;

domain of gof = domain of f

codomain of gof = codomain of g.

Thus;

domain of gof = { 2,4,5 }

codomain of gof = { 2,4 }

We know that;

(gof)(x) = g{f(x)}

Thus,

(gof)(2) = g{f(2)}

= g(3) {using eq-(1)}

= 4 {using eq-(5)}

(gof)(4) = g{f(4)}

= g(6) {using eq-(2)}

= 2 {using eq-(6)}

(gof)(5) = g{f(5)}

= g(2) {using eq-(3)}

= 4 {using eq-(4)}

Hence,

gof = { (2,4) , (4,2) , (5,4) }