MyQuestionIcon

1

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

Definition of Functions

Find the doma...

Question

Find the domain of the function $f (x)$ given by $f (x) = \frac{x - 2}{3 - x}$ .

A

R

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

B

R - Z

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

C

R - {3}

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

D

R - {2}

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

Open in App

Solution

The correct option is C $R - {3}$
Here, $f (x)$ is defined for all x satisfying $3 - x \neq 0$ i.e., $x \neq 3$ .
Hence, Domain (f) = $R - {3}$

Suggest Corrections

thumbs-up

0

Similar questions

Find the domain of the function f(x) = x |x|

Q. The domain of the function f(x) given by

f (x) = \frac{1}{\sqrt{x + | x |}}

Q. The domain and range of the function f given by f(x) = 2 − |x − 5|, is
(a) Domain = R⁺, Range = (−∞, 1]
(b) Domain = R, Range = (−∞, 2]
(c) Domain =R, Range = (−∞, 2)
(d) Domain = R⁺, Range = (−∞, 2]

Q. The domain of the function f(x) given by

f (x) = \frac{1}{\sqrt{x - (x]}}

where [.] is greatest integer function, is

Q. Classify the following functions as injection, surjection or bijection :
(i) f : N → N given by f(x) = x²
(ii) f : Z → Z given by f(x) = x²
(iii) f : N → N given by f(x) = x³
(iv) f : Z → Z given by f(x) = x³
(v) f : R → R, defined by f(x) = |x|
(vi) f : Z → Z, defined by f(x) = x² + x
(vii) f : Z → Z, defined by f(x) = x − 5
(viii) f : R → R, defined by f(x) = sinx
(ix) f : R → R, defined by f(x) = x³ + 1
(x) f : R → R, defined by f(x) = x³ − x
(xi) f : R → R, defined by f(x) = sin²x + cos²x
(xii) f : Q − {3} → Q, defined by

f (x) = \frac{2 x + 3}{x - 3}

(xiii) f : Q → Q, defined by f(x) = x³ + 1
(xiv) f : R → R, defined by f(x) = 5x³ + 4
(xv) f : R → R, defined by f(x) = 3 − 4x
(xvi) f : R → R, defined by f(x) = 1 + x²
(xvii) f : R → R, defined by f(x) =

\frac{x}{x^{2} + 1}

[NCERT EXEMPLAR]

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Definition of Function

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Definition of Functions

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon