# The Relation F is Defined by and the Relation G is Defined by Show that F is a Function and G is Not a Function. - Mathematics

Sum

The relation f is defined by f(x) = {(x^2,0<=x<=3),(3x,3<=x<=10):}

The relation g is defined by  g(x) = {(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}

Show that f is a function and g is not a function.

#### Solution

The relation f is defined as f(x) = {(x^2,0<=x<=3),(3x,3<=x<=10):}

It is observed that for

0 ≤ x < 3, f(x) = x2

3 < x ≤ 10, f(x) = 3x

Also, at x = 3, f(x) = 32 = 9 or f(x) = 3 × 3 = 9

i.e., at x = 3, f(x) = 9

Therefore, for 0 ≤ x ≤ 10, the images of f(x) are unique.

Thus, the given relation is a function.

The relation g is defined as g(f) = {(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}

It can be observed that for x = 2, g(x) = 22 = 4 and g(x) = 3 × 2 = 6

Hence, element 2 of the domain of the relation g corresponds to two different images i.e., 4 and 6. Hence, this relation is not a function.

Concept: Relation
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#### APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 2 Relations and Functions
Exercise 2.4 | Q 1 | Page 46
NCERT Class 11 Mathematics Textbook
Chapter 16 Probability
Q 1 | Page 46