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​

Answer 1

Answer:

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Answer 2

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GIVEN

$1. \: \: \sf{ \: A= \{1,2,0,-1 \} \: \: and \: \: B= \{1,3-1,-3}\}$

$2. \: \: \sf{ The \: function \: f : A \to B\: \: defined \: by }$

$\sf{f(x) = px + q \: }$

$3. \: \: \sf{f= \{ (1,1),(2,3),(0,-1),(-1,-3) \}}$

TO DETERMINE

The Value of p & q

CALCULATION

By the given condition

$\sf{ \: f(1)=1 \: \: and \: \: f(0)=-1}$

So

$\sf{f(x) = px + q \: } \: \: gives$

$\sf{ f(1) = p + q\: }$

$\sf{ f(0) = (p \times 0) + q\: = q \: }$

Therefore

$\sf{ p + q = 1 \: \: \: .......(1)\: }$

$\sf{ q = - 1\: } \: \: ......(2)$

From Equation (1) and Equation (2) we get

$\sf{ p - 1 = 1\: }$

$\implies \: \sf{ p = 2\: }$

Hence the required values of p and q are 2 & - 1 respectively

Also

$\sf{f(x) = 2x - 1\: }$

RESULT

$\boxed{ \sf{ \: \: p = 2 \: \: \: and \: \: q = - 1\: } \: }$

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LEARN MORE FROM BRAINLY

If A ={2,3} and

B= { x | x is solution of x^2 + 5x + 6= 0}

Are there A and B equal set or disjoint set?

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