Et f x - x 2-1- x - g x - x -2- x -3 then domain of f x - g x A- RB- R -0-3C- R -0-2D- R -2-0-3

The correct option is D ℝ { 2, 0, 3}Let h(x)=f(x)g(x) ∴ h(x)=x^2 1xx+2x 3=(x^2 1)(x 3)x(x+2) But for x=3,g(x) not defined Hence h(x) is not defined for x=0, ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Domain

et f x = x 2-...

Question

Let $f (x) = \frac{x^{2} - 1}{x}, g (x) = \frac{x + 2}{x - 3}$ then domain of $\frac{f (x)}{g (x)}$ is

R - {0, - 2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

R - {- 2, 0, 3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

R

No worries! We‘ve got your back. Try BYJU‘S free classes today!

R - {0, - 3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $R - {- 2, 0, 3}$
Let $h (x) = \frac{f (x)}{g (x)}$
$∴ h (x) = \frac{\frac{x^{2} - 1}{x}}{\frac{x + 2}{x - 3}} = \frac{(x^{2} - 1) (x - 3)}{x (x + 2)}$
But for $x = 3, g (x)$ not defined
Hence $h (x)$ is not defined for $x = 0, - 2, 3$
Hence required domain is
$R - {- 2, 0, 3}$

Suggest Corrections

Similar questions

Q. Let

f (x) = x^{2} - 2 x, x \in R

and

g (x) = f (f (x) - 1) + f (5 - f (x))

,show that

g (x) \geq 0, \forall x \in R

Q. If

f (x) = x^{2} + \frac{1}{x^{2}} and g (x) = x - \frac{1}{x}, x ϵ R - {- 1, 0, 1}, and h (x) = \frac{f (x)}{g (x)}

then the local minimum value of

h (x)

Q. Let f(x) = x,

g (x) = \frac{1}{x}

and h(x) = f(x) g(x). Then, h(x) = 1
(a) x ∈ R
(b) x ∈ Q
(c) x ∈ R − Q
(d) x ∈ R, x ≠ 0

$f (x) = \sqrt{x + 1} & g (x) = 2 x - 3$

Find the domain of $\frac{f}{g}$

Let $f (x) = x^{2} - 2 x, x ϵ R$ and $g (x) = f (f (x) - 1) + f (5 - f (x)) .$ Which of the following statements(s) is/are true?

Join BYJU'S Learning Program

Explore more

Domain

Standard XII Mathematics

Join BYJU'S Learning Program

Let f(x)=x2−1x,g(x)=x+2x−3 then domain of f(x)g(x) is

The correct option is B R−{−2,0,3}Let h(x)=f(x)g(x) ∴h(x)=x2−1xx+2x−3=(x2−1)(x−3)x(x+2) But for x=3,g(x) not defined Hence h(x) is not defined for x=0,−2,3 Hence required domain is R−{−2,0,3}

Let $f (x) = \frac{x^{2} - 1}{x}, g (x) = \frac{x + 2}{x - 3}$ then domain of $\frac{f (x)}{g (x)}$ is