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Home » The relation f is defined by (FIG 1) The relation g is defined by(FIG 2).Show that f is a function and g is not a function.
The relation f is defined by (FIG 1) The relation g is defined by(FIG 2).Show that f is a function and g is not a function.
CBSE | Class 11 | Maths | Miscellaneous Exercise | NCERT | Relations and Functions
The relation f is defined by (FIG 1) The relation g is defined by(FIG 2).Show that f is a function and g is not a function.

FIG 1: NCERT Solutions Class 11 Mathematics Chapter 2 ex.misc - 1

FIG 2:NCERT Solutions Class 11 Mathematics Chapter 2 ex.misc - 2

SOLUTION:

The given connection f is characterized as:

NCERT Solutions Class 11 Mathematics Chapter 2 ex.misc - 3

It is seen that, for

    \[0\text{ }\le \text{ }x\text{ }<\text{ }3\]

,

    \[f\left( x \right)\text{ }=\text{ }x2\text{ }and\text{ }for\text{ }3\text{ }<\text{ }x\text{ }\le \text{ }10,\]

    \[f\left( x \right)\text{ }=\text{ }3x\]

Additionally, at

    \[x\text{ }=\text{ }3\]

    \[f\left( x \right)\text{ }=\text{ }32\text{ }=\text{ }9\text{ }or\text{ }f\left( x \right)\text{ }=\text{ }3\text{ }\times \text{ }3\text{ }=\text{ }9\]

i.e., at

    \[~x\text{ }=\text{ }3,\text{ }f\left( x \right)\text{ }=\text{ }9\]

Henceforth, for

    \[0\text{ }\le \text{ }x\text{ }\le \text{ }10\]

, the pictures of f(x) are one of a kind.

In this way, the given connection is a capacity.

Presently,

In the given connection g is characterized as

NCERT Solutions Class 11 Mathematics Chapter 2 ex.misc - 4

It is seen that, for

    \[x\text{ }=\text{ }2\]

    \[g\left( x \right)\text{ }=\text{ }22\text{ }=\text{ }4\text{ }and\text{ }g\left( x \right)\text{ }=\text{ }3\text{ }\times \text{ }2\text{ }=\text{ }6\]

Subsequently, component 2 of the space of the connection g compares to two distinct pictures i.e., 4 and 6.

Hence, this connection isn’t a capacity.

i

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