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  • Can someone help me with this, - Sets, Relations and Functions - JEE Main

The range of the function f\left ( x \right )= ^{7-x}P_{x-3} is

  • Option 1)

    \left \{ 1,2,3,4 \right \}

  • Option 2)

    \left \{ 1,2,3,4,5,6 \right \}

  • Option 3)

    \left \{ 1,2,3 \right \}

  • Option 4)

    \left \{ 1,2,3,4,5\right \}

 

Answers (2)

best_answer

As we learnt in

Range -

The range of the relation R is the set of all second elements of the ordered pairs in a relation R.

- wherein

eg. R={(a,b),(c,d)}. Then Range is {b,d}

 

 f(x)=\ ^{7-x}P_{n-3}

Now, 7-x\leq x-3, \, \, \, \, \, 7-x > 0

        10\leq2\pi, \, \, \, \, \, x < 7

        10\geq5, \, \, \, \, \, x - 3 \geq0

\therefore\ \, \, x=3,4,5

\therefore\ \, \, ^{7-3}P_{3-3}, \, \, ^{4}P_{0}=1, \, \, \, ^{3}P_{1}=3, \, \, \, ^{2}P_{2}=2

\therefore    Range = {1, 2, 3,}

Correct option is 3.

 

 


Option 1)

\left \{ 1,2,3,4 \right \}

This is an incorrect option.

Option 2)

\left \{ 1,2,3,4,5,6 \right \}

This is an incorrect option.

Option 3)

\left \{ 1,2,3 \right \}

This is the correct option.

Option 4)

\left \{ 1,2,3,4,5\right \}

This is an incorrect option.

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