Find the domain of $f (x) =^{(3 x - 1)} P_{(20 - 4 x)}$

Open in App

Solution

$f (x) =^{(3 x - 1)} P_{(20 - 4 x)}$

We know that, in $^{n} P_{r}$
$n \geq r$ and $n \geq 0$ and $r \geq 0$
$∴ 3 x - 1 \geq 20 - 4 x$

$\Rightarrow 7 x \geq 21 \Rightarrow x \geq 3$ ...... $(1)$

Also, $3 x - 1 \geq 0 \Rightarrow x \geq \frac{1}{3}$ ...... $(2)$

And $20 - 4 x \geq 0 \Rightarrow x \leq 5$ ....... $(3)$

Which is possible if and only if $x$ is an integer taking above in account

we find $x$ should be an integer.Thus domain of $f (x) = {3, 4, 5}$

Suggest Corrections

Similar questions

f (x) = \frac{x^{2} - 3 x + 1}{x^{2} + 4 x + 3},

f (x)

f (x) = 4 x + 3

f (x) = \frac{1}{\sqrt{x^{2} - 4 x}}

f (x) = \frac{1}{| 3 x - 27 |}

R - {a}

a

Join BYJU'S Learning Program