If fx- a-b x- x1 -is continuous at x -1 then the value of a - b is A- a-4- b-4B- a -4- b -0C- a -0- b -4D- a-2- b-2

The correct option is C a=0, b= 4Since f(x) is continuous at x=1 Therefore, f(1)=lim_x→ 1^+ f(x)=lim_x→ 1^ f(x) so,f(1)=4=lim_x→ 1^ f(x)=a+bx.....(1) and ...

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

Byju's Answer

Standard XII

Mathematics

Algebra of Limits

If fx=[ a+b x...

Question

If $f (x) = ⎧ ⎨ ⎩ \begin{matrix} a + b x, x < 1 4 x = 1 b - a x, x > 1 \end{matrix}$
is continuous at $x = 1$ then the value of $a, b$ is

a = 4, b = 0

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

a = - 4, b = 4

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

a = 0, b = - 4

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

a = 2, b = - 2

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

Open in App

Solution

The correct option is C $a = 0, b = - 4$
Since $f (x)$ is continuous at $x = 1$
Therefore,
$f (1) = lim x \to 1^{+} f (x) = lim x \to 1^{-} f (x)$
so, $f (1) = 4 = lim x \to 1^{-} f (x) = a + b x . . . . . (1)$
and $f (1) = 4 = lim x \to 1^{+} f (x) = b - a x . . . (2)$
Solving equation $(1)$ and $(2)$ , we get
$a = 0$ and $b = 4$

Suggest Corrections

Similar questions

Q. Let

f (x) = \{\begin{matrix} \frac{x - 4}{|x - 4|} + a, & x < 4 \\ a + b, & x = 4 \\ \frac{x - 4}{|x - 4|} + b, & x > 4 \end{matrix} .

Then, f (x) is continuous at x = 4 when
(a) a = 0, b = 0
(b) a = 1, b = 1
(c) a = −1, b = 1
(d) a = 1, b = −1.

Q. Let

f (x) = ⎧ ⎨ ⎩ \begin{matrix} a - b x, & x < 1 4, & x = 1 b + a x, & x > 1 \end{matrix}

.
If

f (x)

is continuous at

x = 1,

then the value of

a^{2} + b^{2}

is equal to

Q. If

f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{x^{2}}{a}; 0 \leq x < 1 - 1; 1 \leq x < \sqrt{2} \frac{2 b^{2} - 4 b}{x^{2}}; \sqrt{2} \leq x < \infty \end{matrix}

then find the value of

a

and

b

f (x)

is continuous in

[0, \infty)

.Find

a + b

consider the function
$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} a + b x, x < 1 4, x = 1 b - a x, x > 1 \end{matrix}$
If ${lim}_{x \to 1} f (x) = f (1)$ , then the values of a and b are

Q. Let

f (x) = {\begin{matrix} a x, x < 2 a x^{2} - b x + 3, x \geq 2 \end{matrix}

If f(x) is differentiable for all x, then

Join BYJU'S Learning Program

If f(x)=⎧⎨⎩a+bx, x<1 4 x=1b−ax, x>1 is continuous at x=1 then the value of a,b is

The correct option is C a=0, b=−4Since f(x) is continuous at x=1 Therefore, f(1)=limx→1+f(x)=limx→1−f(x) so,f(1)=4=limx→1−f(x)=a+bx.....(1) and f(1)=4=limx→1+f(x)=b−ax...(2) Solving equation (1) and (2), we get a=0 and b=4

If $f (x) = ⎧ ⎨ ⎩ \begin{matrix} a + b x, x < 1 4 x = 1 b - a x, x > 1 \end{matrix}$
is continuous at $x = 1$ then the value of $a, b$ is