f x - eft matrix 3 x-5 - if - x geq 2 X - 2- - if - X -2 1Discuss the continuity of f x at x -2-

We have, f(x)={ 3x+5 amp;if x≥2 x^2, amp;if x lt;2 . At x=2, LHL=x→ 2^ lim(x)^2 =h→ 0lim(2 h)^2=h→ 0lim(4+h^2 4h)=4 and RHL= x→ 2'lim(3x+5) =h→ 0lim ...

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

Byju's Answer

Standard XII

Mathematics

Composite Function

f x = eft ma...

Question

$f (x) = {\begin{matrix} 3 x + 5 & i f x \geq 2 x^{2}, & i f x < 2 \end{matrix}$

Discuss the continuity of f(x) at x=2.

Open in App

Solution

We have, $f (x) = {\begin{matrix} 3 x + 5 & i f x \geq 2 x^{2}, & i f x < 2 \end{matrix}$
At x=2, $L H L = l i m x \to 2^{-} (x)^{2}$
$= l i m h \to 0 (2 - h)^{2} = l i m h \to 0 (4 + h^{2} - 4 h) = 4$
and $R H L = l i m x \to 2^{'} (3 x + 5) = l i m h \to 0 [3 (2 + h) + 5] = 11$
Since, LHL $\neq$ RHL at x=2
So, f(x)is discontinuous at x=2,

Suggest Corrections

Similar questions

Q. Let

f (x) = {\begin{matrix} x^{p} s i n \frac{1}{x}, & x \neq 0 0, & x = 0 \end{matrix}

then f(x) is continuous but not differential at x = 0 if

Q. Find 'a' and 'b', if the function given by

f (x) = {\begin{matrix} a x^{2} + b, i f x < 1 2 x + 1, i f x \geq 1 \end{matrix}

is differentiable at x = 1.

$f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 2^{x + 2} - 16 & i f x \neq 2 \begin{matrix} 4^{x} - 16 k \end{matrix} & i f x = 2 \end{matrix} a t x = 2$

If f(x) is continuous at x=2, then find the value of k.

Find the values of a and b so that the function defined by f(x) = ${\begin{matrix} a x + 1, i f x \leq 3 b x + 3, i f x > 3 \end{matrix}$ is continuous at x=3.

Q. If

f (x) = {\begin{matrix} \frac{x^{2} - 1}{x + 1}, & w h e n x \neq - 1 - 2, & w h e n x = - 1 \end{matrix}

, then

Join BYJU'S Learning Program

f(x)={3x+5if x≥2x2,if x<2 Discuss the continuity of f(x) at x=2.

We have, f(x)={3x+5if x≥2x2,if x<2 At x=2, LHL=limx→2−(x)2 =limh→0(2−h)2=limh→0(4+h2−4h)=4 and RHL=limx→2′(3x+5)=limh→0[3(2+h)+5]=11 Since, LHL ≠ RHL at x=2 So, f(x)is discontinuous at x=2,

$f (x) = {\begin{matrix} 3 x + 5 & i f x \geq 2 x^{2}, & i f x < 2 \end{matrix}$

Discuss the continuity of f(x) at x=2.