Home
PYQ PracticeFree
JEE Rank Predictor
Answer Key

Mathematics - Continuity - Differentiability Question with Solution | TestHub

MathematicsContinuity - DifferentiabilityMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Column -1 contains information about g(f(x))

Column -2 contains information about interval of g(f(x)).

Column -3 contains information about continuity and differentiability of $g (f (x))$ in R Match the following Column(s)

Which of the following is the only correct combination?

Options:

Answer:

Solution:

$g (f (x)) = ⎩ ⎨ ⎧ x + a + 1 (x + a - 1)^{2} + b x^{2} + b (x - 2)^{2} + b x < - a - a \leq x < 0 0 \leq x < 1 x \geq 1$

Now for $a = 1$ , $b = 0$ , $g (f (x))$ is continuous for all $x \in R$ and for $a = 1$ , $b = 0$ , $g (f (x))$ is non-differentiable at $x = \pm 1$ .

Stream:JEESubject:MathematicsTopic:Continuity - DifferentiabilitySubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...

Mathematics - Continuity - Differentiability Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main + Advanced (1 year 12th class)

JEE Advanced (2028)