Name: Algebraic Operations: Functions
Uploaded: 2019-07-19
Duration: 7 min 10 s
Description: Now that we know what functions are, what can we do with them? Can we do operations with them? Yes! What won't these functions do? Let us learn more here.

Question

Check whether the followings represent function or not.

(i) $x^{2} + y^{2} = 36$ , $y \in [0, 6]$ (ii) $x^{2} + y^{2} = 36, x \in [0, 1]$

(iii) $x^{2} + y^{2} = 36, x \in [- 6, 6]$ (iv) $x^{2} + y^{2} = 36$ .

Accepted Answer

A function is a relation between two non-empty sets $A & B$ , such that each element of $A$ , is related to one and only one element of sets $B$ . So in simple language every input of $A$ , we will get unique out in $B$ .

This types of problems we can do it graphically, Following these steps, we can determine graphically that whether a given relation is function or not.

So,

$S t e p - 1 \to$ Draw the graph of a given relation.

$S t e p - 2 \to$ Take line parallel to $y - a x i s$ .

If a line intersects at a single point then given relation is a function otherwise relation.

So, applying the above method in following problems

(i) Draw the graph of $x^{2} + y^{2} = 36$ in $y \in [0, 6]$ , we get (Graph is a half circle)

By looking graph, we can say that the line parallel to $y - a x i s$ , intersects at a single point, so given relation is a function.

(ii) Draw the graph of $x^{2} + y^{2} = 36, x \in [0, 1]$ ,we get,

(Graph is in part of the circle)

A line parallel to $y - a x i s$ , intersecting the graph at two points, so given relation is not a function.

(iii) Draw the graph of $x^{2} + y^{2} = 36, x \in [- 6, 6]$ ,we get,

A line parallel to the $y - a x i s$ , intersects at two points, so given relation is not a function.

(iv) Draw the graph of $x^{2} + y^{2} = 36$ ,we get,

A line parallel to the intersects $y - a x i s$ , at two points, so given relation is not a function.

Check whether the followings represent function or not.

(i) $x^{2} + y^{2} = 36$ , $y \in [0, 6]$ (ii) $x^{2} + y^{2} = 36, x \in [0, 1]$

(iii) $x^{2} + y^{2} = 36, x \in [- 6, 6]$ (iv) $x^{2} + y^{2} = 36$ .

Important Questions on Functions

Learn and Prepare for any exam you want !

Check whether the followings represent function or not. (i) x2+y2=36, y∈[0,6] (ii) x2+y2=36, x∈[0,1] (iii) x2+y2=36, x∈[-6,6] (iv) x2+y2=36.

Important Questions on Functions

Learn and Prepare for any exam you want !

Check whether the followings represent function or not.

(i) $x^{2} + y^{2} = 36$ , $y \in [0, 6]$ (ii) $x^{2} + y^{2} = 36, x \in [0, 1]$

(iii) $x^{2} + y^{2} = 36, x \in [- 6, 6]$ (iv) $x^{2} + y^{2} = 36$ .