Question

Find domein of 1/6x-x^2-5

Answer 1

Step-by-step explanation:

given,

f(x)=1/6x-x^2-5

therefore,

6x-x^2-5≠0

x^2-6x+5≠0

x^2-x-5x+5≠0

x(x-1)-5(x-1)≠0

(x-5)(x-1)≠0

x≠1,5

domain is R-{1,5}

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

The given function is

$\displaystyle \: f(x) = \frac{1}{6x - {x}^{2} - 5 }$

Now the function is not defined where denominator vanishes

That is

$6x - {x}^{2} - 5 = 0$

$\implies \: {x}^{2} - 6x + 5 = 0$

$\implies \: {x}^{2} - 5x - x+ 5 = 0$

$\implies \: {x}( x - 5) - 1(x - 5) = 0$

$\implies \: ( x - 5) (x - 1) = 0$

Which gives x = 1 , 5

So the required Domain of the function is

$\mathbb{R} \: - \{ \: \:1 , 5 \: \}$