Let f- be difined as fx-2sin - x2 - if x1-If fx is continuous on - then a-b equals-

If f is continuous at x= 1, then nbsp; f( 1^ )=f( 1) ⇒ 2=|a 1+b| ⇒ |a+b 1|=2...(i) Similarly, f(1^ )=f(1) ⇒ |a+b+1|=0 ⇒ a+b= 1 ...

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

Byju's Answer

Standard XII

Mathematics

Domain

Let f:ℝ→ℝ be ...

Question

Let $f : R \to R$ be difined as $f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 2 sin (- \frac{π x}{2}), & if x < - 1 | a x^{2} + x + b |, & if - 1 \leq x \leq 1 sin (π x) & if x > 1 \end{matrix}$ .
If $f (x)$ is continuous on $R,$ then $a + b$ equals:

3

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

- 1

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

- 3

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

1

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

Open in App

Solution

The correct option is B $- 1$
If $f$ is continuous at $x = - 1$ , then
$f (- 1^{-}) = f (- 1)$
$\Rightarrow 2 = | a - 1 + b |$
$\Rightarrow | a + b - 1 | = 2... (i)$
Similarly,
$f (1^{-}) = f (1)$
$\Rightarrow | a + b + 1 | = 0$
$\Rightarrow a + b = - 1$

Suggest Corrections

Similar questions

Q. Let

f : R \to R

be a continuous function satisfying

f (0) = 1

and

f (2 x) - f (x) = x

, for all

x \in R .

Then

f (2020)

equals

Q. Let a function

f : R \to R

be defined as

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} sin x - e^{x} & if x \leq 0 a + [- x] & if 0 < x < 1 2 x - b & if x \geq 1 \end{matrix}

where

[x]

is the greatest integer less than or equal to

x

. If

f

is continuous on

R

, then

(a + b)

is equal to

Q. Let

f : R \to R

be a continuous function such that

f (x) + f (x + 1) = 2,

for all

x \in R .

I_{1} = \int_{0}^{8} f (x) d x

and

I_{2} = \int_{- 1}^{3} f (x) d x

then the value of

I_{1} + 2 I_{2}

is equal to

Q. Let

f : R \to R

be defined by

f (x) = \frac{1}{x} \forall x \in R,

then

f

Q. Let

f : R \to R

be defined as

f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{x^{3}}{(1 - cos 2 x)^{2}} \cdot {log}_{e} (\frac{1 + 2 x e^{- 2 x}}{(1 - x e^{- x})^{2}}) & , & x \neq 0 α & , & x = 0 \end{matrix}

f

is continuous at

x = 0

, then

α

is equal to:

Join BYJU'S Learning Program

Let f:R→R be difined as f(x)=⎧⎪ ⎪ ⎪ ⎪⎨⎪ ⎪ ⎪ ⎪⎩2sin(−πx2),if x<−1|ax2+x+b|,if −1≤x≤1sin(πx)if x>1. If f(x) is continuous on R, then a+b equals:

The correct option is B −1If f is continuous at x=−1, then f(−1−)=f(−1) ⇒2=|a−1+b| ⇒|a+b−1|=2...(i) Similarly, f(1−)=f(1) ⇒|a+b+1|=0 ⇒a+b=−1

Let $f : R \to R$ be difined as $f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} 2 sin (- \frac{π x}{2}), & if x < - 1 | a x^{2} + x + b |, & if - 1 \leq x \leq 1 sin (π x) & if x > 1 \end{matrix}$ .
If $f (x)$ is continuous on $R,$ then $a + b$ equals:

The correct option is B $- 1$
If $f$ is continuous at $x = - 1$ , then
$f (- 1^{-}) = f (- 1)$
$\Rightarrow 2 = | a - 1 + b |$
$\Rightarrow | a + b - 1 | = 2... (i)$
Similarly,
$f (1^{-}) = f (1)$
$\Rightarrow | a + b + 1 | = 0$
$\Rightarrow a + b = - 1$