CameraIcon

SearchIcon

MyQuestionIcon

1

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

Theorems for Continuity

Let fx=[x] ...

Question

Let $f (x) = [x]$ and $g (x) = {\begin{matrix} 0, x \in Z x^{2}; x \in R - Z \end{matrix}$ , then $g \circ f$ is continuous for $x \in A$ . (where $[.]$ denotes greatest integer function), find $A$ ?

Open in App

Solution

As image set of [.] (G.I.F.) function
only contains integers and g(n)=0
when $x ϵ z$ , therefore, go f(x)=0 for
$\forall x ϵ R \Rightarrow A \equiv R$ (set of real numbers)

Suggest Corrections

thumbs-up

0

Similar questions

f (x) = [x]

g (x) = s g n (x)

[\cdot]

denotes greatest integer function), then discuss the continuity of

f (x) \pm g (x)

f (x) . g (x)

\frac{f (x)}{g (x)}

x = 0

.

f (x) = [x]

g (x) = {\begin{matrix} 0, & x \in Z x^{2}, & x \in R - Z \end{matrix}

. Then which of the following is not true ([.] represents the greatest integer function)?

f (x) = x^{2} - 1

g (x) = {\begin{matrix} [| f (| x |) |] + | [f (x)] |, & x \in (- 1, 0) \cup (0, 1) 1 & o t h e r w i s e \end{matrix}

.
Then find the range of

ln ([| g (x) |]),

[.]

denotes the greatest integer function

f

R \to R, g : R \to R

f (x) = | x |, g (x) = [x] \forall x \in R

[x]

denotes greatest integer function. The set of values of

x

g [f (x)] \leq f [g (x)]

is satisfied is given by

f (x) = sin \frac{π}{2} x

g (x) = [x],

where [.] denotes greatest integer function, then

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Algebra of Continuous Functions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Theorems for Continuity

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon