The number of integers in the range of f x - -19 x 2-6 x -1 isA- 3B- 4C- 1D- 2

The correct option is A 3Let t=9x^2+6x 1⇒ t=(3x+1)^2 2 ⇒ t≥ 2 For f(x) to be defined, t∈ [ 2, 1]∪[1,∞) ⇒^ 1 (t)∈[0,π2)∪[2π3,π] Integers in the range of f(x) ar ...

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

Byju's Answer

Standard XII

Mathematics

Expressing x in Terms of y, to Find the Range of a Function

The number of...

Question

The number of integers in the range of $f (x) = {sec}^{- 1} (9 x^{2} + 6 x - 1)$ is

1

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

2

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

3

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

4

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

Open in App

Solution

The correct option is C $3$
Let $t = 9 x^{2} + 6 x - 1 \Rightarrow t = (3 x + 1)^{2} - 2$
$\Rightarrow t \geq - 2$
For $f (x)$ to be defined, $t \in [- 2, - 1] \cup [1, \infty)$
$\Rightarrow {sec}^{- 1} (t) \in [0, \frac{π}{2}) \cup [\frac{2 π}{3}, π]$
Integers in the range of $f (x)$ are $0, 1, 3$

Suggest Corrections

Similar questions

Q. The range of the function

f (x) = \frac{x + 3}{| x + 3 |}, x \neq - 3

f (x)

is a real valued function

& f (x) = [{log}_{\sqrt{2}} (sin (ln (\frac{\sqrt{4 - x^{2}}}{1 - x})) + cos (ln (\frac{\sqrt{4 - x^{2}}}{1 - x})))]

where [.] denotes the greatest integer function.
Then which of the following statements are true?

The degree of the polynomial $2 - 8 x^{0} y z^{3} + x y + 4 x y z$ is ___

Q. The number of integers which do not satisfy the given equation

| x - 1 | + | x - 2 | + | x - 3 | \geq 6

Q. If

f (x) = x^{3} + 3 x^{2} + 4 x + a s i n x + b c o s x \forall x ϵ R

is one - one function then the maximum value of

a^{2} + b^{2}

Join BYJU'S Learning Program

The number of integers in the range of f(x)=sec−1(9x2+6x−1) is

The correct option is C 3Let t=9x2+6x−1⇒t=(3x+1)2−2 ⇒t≥−2 For f(x) to be defined, t∈[−2,−1]∪[1,∞) ⇒sec−1(t)∈[0,π2)∪[2π3,π] Integers in the range of f(x) are 0, 1, 3

The number of integers in the range of $f (x) = {sec}^{- 1} (9 x^{2} + 6 x - 1)$ is