# The range of the function $\dpi{100} f\left ( x \right )= ^{7-x}P_{x-3}$ 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) $\left \{ 1,2,3,4,5\right \}$

N neha
P Plabita

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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