Fsc Part 1 Mathematics (Complete Solution)

Q4
Find the inverse of each of the following relations.tell whether each relation and its inverse is a function or not

(i) {(2,1),(3,2),(4,3),(5,4),(6,5)}

Solution:

Let A={(2,1,),(3,2),(4,3),(5,4),(6,5)},the inverse of A which are

A-1={(1,2),(2,3),(3,4),(4,5),(5,6)}

A is a function and the A-1(inverse of A) is also a function.

(ii) {(1,3),(2,5),(3,7),(4,9),(5,11)}

Solution:

Let B={{(1,3),(2,5),(3,7),(4,9),(5,11)},the inverse of B which is

B-1={(3,1),(5,2),(7,3),(9,4),(11,5)}

B is a function and B-1is also a function.

(iii) {(x,y) l y=2x+3,x∈R}

Solution:

Let C={(x,y) l y=2x+3,x∈R}={(0,3),(1,5),(2,7)}

C is a function

C-1={(x,y) l y=(x-3)÷2,x∈R}

and C-1 is also a function.

(iv) {(x,y) l y2=4ax,x≥0}

Solution:

Let D={(x,y) l y2=4ax,x≥0}

D-1 = {(x,y) l y =
1
 4a
x2, x 0 }

D is not a function but the D-1(inverse of D) is a function.

(v) {(x,y) l x2+y2=9, l x l ≤3,l y l ≤ 3}

Solution:

let E={(x,y) l x2+y2=9, l x l ≤3,l y l ≤ 3}

E-1= {(x,y) l y2+x2=9, l x l ∧ l y l ≤ 3}

E and E-1 are not functions.

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