<p><strong>Let <math><mrow><mi>f</mi><mo>=</mo><mrow><mo>{</mo><mrow><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mn>3</mn><mo>,</mo><mn>5</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mn>4</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow></mrow><mo>}</mo></mrow></mrow></math> and <math><mrow><mi>g</mi><mo>=</mo><mrow><mo>{</mo><mrow><mrow><mo>(</mo><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mn>5</mn><mo>,</mo><mn>1</mn></mrow><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mrow><mn>1</mn><mo>,</mo><mn>3</mn></mrow><mo>)</mo></mrow></mrow><mo>}</mo></mrow></mrow></math> . Then <math><mrow><mi>g</mi><mo>∘</mo><mi>f</mi><mo>=</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo></mrow></math> and <math><mrow><mi>f</mi><mo>∘</mo><mi>g</mi><mo>=</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>.</mo></mrow></math></strong></p>

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Let $f = {(1, 2), (3, 5), (4, 1)}$ and $g = {(2, 3), (5, 1), (1, 3)}$ . Then $g \circ f =$ and $f \circ g =__.$

3 Views | Posted 3 months ago

Answered by

alok kumar singh | Contributor-Level 10

3 months ago

This is a Fill in the Blanks Type Question as classified in NCERT Exemplar

Sol:

$\begin{array}{l} \end{array} G i v e n t h a t, f = {(1, 2), (3, 5), (4, 1)} a n d g = {(2, 3), (5, 1), (1, 3)}$

$g o f (1) = g {f (1)} = g (2) = 3$

$g o f (3) = g {f (3)} = g (5) = 1$

$g o f (4) = g {f (4)} = g (1) = 3$

$\begin{array}{l} ∴ g o f = {(1, 3), (3, 1), (4, 3)} \end{array}$

$\begin{array}{l} \end{array} f o g (2) = f {g (2)} = f (3) = 5$

$f o g (5) = f {g (5)} = f (1) = 2$

$f o g (1) = f {g (1)} = f (3) = 5$

$∴ f o g = {(2, 5), (5, 2), (1, 5)}$

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