Let f- be given by fx-5x- x- x2-6- x- Then

Let f(x) be continuous at x=c, c∈ℚ ⇒lim_x→ c f(x) =f(c) ⇒lim_x→ cx^2+6=5c nbsp;⇒ c^2 5c+6=0 ⇒ nbsp; c=2,3 ∴ f(x) is continuous at x=2 and x=3 only ...

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Standard XII

Mathematics

Range

Let f:ℝ→ℝ be ...

Question

Let $f : R \to R$ be given by $f (x) = {\begin{matrix} 5 x, & x \in Q x^{2} + 6, & x \in R - Q \end{matrix} .$ Then

f

is continuous at

x = 2

and

x = 3

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f

is not continuous at

x = 2

and

x = 3

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f

is continuous at

x = 2

but not at

x = 3

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f

is continuous at

x = 3

but not at

x = 2

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Solution

The correct option is A $f$ is continuous at $x = 2$ and $x = 3$
Let $f (x)$ be continuous at $x = c, c \in Q$
$\Rightarrow lim x \to c f (x) = f (c)$
$\Rightarrow lim x \to c x^{2} + 6 = 5 c$
$\Rightarrow c^{2} - 5 c + 6 = 0$
$\Rightarrow c = 2, 3$
$∴ f (x)$ is continuous at $x = 2$ and $x = 3$ only

Suggest Corrections

Similar questions

Q. Let

a \in R

and let

f : R \to R

be given by

f (x) = x^{5} - 5 x + a

Then

Q. Two functions

f : R \to R, g : R \to R

are defined as follows

f (x) = {\begin{matrix} 0, & x \in Q 1, & x \notin Q \end{matrix}

g (x) = {\begin{matrix} - 1 & x \in Q 0, & x \notin Q \end{matrix}

, then

g (f (e)) + f (g (π)) =

Q. Let

R_{1}

and

R_{2}

be two relations defined as follows:

R_{1} = {(a, b) \in R^{2} : a^{2} + b^{2} \in Q}

and

R_{2} = {(a, b) \in R^{2} : a^{2} + b^{2} \notin Q} .

Then

Q. Let

R

be a relation from

Q

Q

defined by

R = {(a, b) : a, b \in Q and a - b \in Z}

.
Show that:

(i) (a, a) \in R

for all

a \in Q

(i i) (a, b) \in R

implies that

(b, a) \in R

(i i i) (a, b) \in R and (b, c) \in R

implies that

(a, c) \in R

Q. Let

f : R \to R

be defined by

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

then

f

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Standard XII Mathematics

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Let f:R→R be given by f(x)={5x,x∈Qx2+6,x∈R−Q. Then

The correct option is A f is continuous at x=2 and x=3Let f(x) be continuous at x=c,c∈Q ⇒limx→cf(x)=f(c) ⇒limx→cx2+6=5c ⇒c2−5c+6=0 ⇒c=2,3 ∴f(x) is continuous at x=2 and x=3 only

Let $f : R \to R$ be given by $f (x) = {\begin{matrix} 5 x, & x \in Q x^{2} + 6, & x \in R - Q \end{matrix} .$ Then