Question

let A= {1,2,0,-1} ,B={1,3,-1,-3} and function f.A To B
F(x) = px+q .if f={ (1,1) ,(2,3) ,(0,-1),(-1,-3)}
find the value of p and q
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Answer 1

GIVEN :

Let A= {1,2,0,-1} , B={1,3,-1,-3} and function f: A To B

f(x) = px+q, if f={(1,1) ,(2,3) ,(0,-1),(-1,-3)}  find the value of p and q

TO FIND :

The values of p and q

SOLUTION :

Given let A= {1,2,0,-1} , B={1,3,-1,-3} and function f: A To B  is defined by

f(x) = px+q, if f={(1,1) ,(2,3) ,(0,-1),(-1,-3)}

From the given function f(x)=px+q

We know y=f(x)=px+q

y=px+q

Now for (1,1)

1=p(1)+q

1=p+q

$p+q=1\hfill (1)$

Now for (2,3)

3=p(2)+q

3=2p+q

$2p+q=3\hfill (2)$

Solving the equations (1) and (2),

Subtracting the equations (1) and (2)

p+q=1

2p+q=3

(-)_(-)_(-)___

-p=-2

⇒ p=2

Substitute the value of p=2 in the equation (1)

2+q=1

q=1-2

⇒ q=-1

∴ the values are p=2 and q=-1