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Standard XII

Mathematics

Definition of Functions

If f1x and ...

Question

If $f_{1} (x)$ and $f_{2} (x)$ are defined on domains $D_{1}$ and $D_{2}$ respectively, then $f_{1} (x) + f_{2} (x)$ is defined on $D_{1} \cap D_{2}$ .

True

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False

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Solution

The correct option is A True
True , because both the functions are required to be defined in the intersection of the domains of individual functions.

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Similar questions

Q. If

f_{1} (x)

and

f_{_{2}} (x)

are defined on domains

D_{1}

and

D_{2}

respectively, then

f_{1} (x) + f_{2} (x)

is defined on

D_{1} \cup D_{2} .

True or false?
If true enter 1 else 0.

Q. Give examples of two one-one functions f₁ and f₂ from R to R, such that f₁ + f₂ : R → R. defined by (f₁ + f₂) (x) = f₁ (x) + f₂ (x) is not one-one.

Q. A function

f (x) = \sqrt{1 - 2 x} + x

is defined from

D_{1} \to D_{2}

and is onto. If the set

D_{1}

is its complete domain then the set

D_{2}

Q. Let

f (x) = a^{x} (a > 0)

be written as

f (x) = f_{1} (x) + f_{2} (x)

, where

f_{1} (x)

is an even function and

f_{2} (x)

is an odd function. Then

f_{1} (x + y) + f_{1} (x - y)

equals :

If $f_{1} (x) = x^{2} + 11 x + n$ and $f_{2} (x) = x$ , then the largest positive integer n for which the equation $f_{1} (x) = f_{2} (x)$ has two distinct real roots, is___

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If f1(x) and f2(x) are defined on domains D1 and D2 respectively, then f1(x)+f2(x) is defined on D1∩D2.

The correct option is A TrueTrue , because both the functions are required to be defined in the intersection of the domains of individual functions.

If $f_{1} (x)$ and $f_{2} (x)$ are defined on domains $D_{1}$ and $D_{2}$ respectively, then $f_{1} (x) + f_{2} (x)$ is defined on $D_{1} \cap D_{2}$ .

The correct option is A True
True , because both the functions are required to be defined in the intersection of the domains of individual functions.