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Continuity of Composite Functions

The compositi...

Question

The composition of two continuous function is a continuous function

A

True

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B

False

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Solution

The correct option is A True

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Similar questions

Q. Prove that composition of two continuous function is continuous.

Q. Assertion :Let

f : R \to R

be any function. Define

g : R \to R

g (x) = | f (x) |

x

g

is continuous is

f

is continuous. Reason: Composition of two continuous functions is a continuous function

Is the function defined by

a continuous function?

Q. If the function u=f(x) is continuous at the point

x = a

and the
function

y = g (u)

is continuous at the point

u = f (a)

, then the
composite function

y = (g o f) (x) = g (f (x))

Show that the function defined by is a continuous function.

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