- Domain of the function- y - - 1 - 2 log 4 16 - log 8 x 2 - 4 x - 3 is -

The correct option is B [ 1,1 ] ∪ ( 3,5 ] since function inside log must be ≥ 0 x ^ 2 4x + 3≥ 0 (x 3)(x 1)≥ 0 ...

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

Byju's Answer

Standard XII

Mathematics

Definition of Functions

[ ...

Question

$\begin{matrix} Domain of the function y = \sqrt[4]{\frac{1}{2} {log}_{4} 16 - {log}_{8} (x^{2} - 4 x + 3)} is \end{matrix}$

[- 1, 1] \cup (3, 5]

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

[- 1, 1] \cup [3, 5]

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

[- 1, 1) \cup (3, 5]

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

None

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

Open in App

Solution

The correct option is B $[- 1, 1] \cup (3, 5]$
$s i n c e f u n c t i o n i n s i d e l o g m u s t b e \geq 0 x^{2} - 4 x + 3 \geq 0 (x - 3) (x - 1) \geq 0 x \in (- \infty, 1] \cup [3, \infty) a l s o i n s i d e o f a r o o t m u s t b e p o s i t i v e, 1 - {log}_{8} (x^{2} - 4 x + 3) \geq 0 1 \geq {log}_{8} (x^{2} - 4 x + 3) 8 \geq x^{2} - 4 x + 3 x^{2} - 4 x - 5 \leq 0 (x - 5) (x + 1) \leq 0 x \in [- 1, 5] h e n c e f r o m t h e g i v e n c o n d i t i o n s, d o m a i n o f t h e f u n c t i o n i s [- 1, 1] \cup (3, 5]$

Suggest Corrections

Similar questions

Q. The domain of

\cos^{- 1} (x^{2} - 4)

is
(a) [3, 5]
(b) [−1, 1]
(c)

[- \sqrt{5}, - \sqrt{3}] \cup [\sqrt{3}, \sqrt{5}]

(d)

[- \sqrt{5}, - \sqrt{3}] \cap [\sqrt{3}, \sqrt{5}]

Q. If

(1, 1)

and

(- 3, 5)

are vertices of a diagonal of a square, then the equations of its sides through

(1, 1)

are

Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the following sets are functions from X to Y.
(i) $f_{1} = {(1, 1), (2, 11), (3, 1), (4, 15)}$
(ii) $f_{2} = {(1, 1), (2, 7), (3, 5)}$
(iii) $f_{3} = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}$

Q. Let X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16}
Determine which of the following sets are functions from X to Y.

(a) f₁ = {(1, 1), (2, 11), (3, 1), (4, 15)}
(b) f₂ = {(1, 1), (2, 7), (3, 5)}
(c) f₃ = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}

Q. If

g (x) = α x + β

,and

g = {(1, 1), (2, 3), (3, 5), (4, 7)}

,then the values of

α, β

are:

Join BYJU'S Learning Program

Domain of the function y=4√12log416−log8(x2−4x+3) is

$\begin{matrix} Domain of the function y = \sqrt[4]{\frac{1}{2} {log}_{4} 16 - {log}_{8} (x^{2} - 4 x + 3)} is \end{matrix}$