Let X -2-3-4-5 and Y -7-9-11-13-15-17- Define a relation f from X to Y by-f - x - y - x - X - y - Y and y -2 x -3i Write f in roster form-ii Find domf and range f-iii Show that f is a function from X to Y-

Let X={2,3,4,5} and Y = 2x+3. Now, x=2 ⇒ y = (2 × 2 + 3) = 7, x = 3 ⇒ y = (2 × 3 +3) = 9, x = 4 ⇒ y = (2 × 4 +3) = 11, x = 5 ⇒ y = (2 × 5 +3) = 13, (i) ∴ f = {( ...

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Byju's Answer

Standard XI

Mathematics

Range

Let X =2,3,4,...

Question

Let $X = {2, 3, 4, 5}$ and $Y = {7, 9, 11, 13, 15, 17}$ . Define a relation f from X to Y by:
$f = {(x, y) : x ϵ X, y ϵ Y and y = 2 x + 3}$

(i) Write f in roster form.

(ii) Find dom(f) and range (f).

(iii) Show that f is a function from X to Y.

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Solution

Let $X = {2, 3, 4, 5}$ and $Y = 2 x + 3$ .

Now, $x = 2 \Rightarrow y = (2 \times 2 + 3) = 7$ ,

$x = 3 \Rightarrow y = (2 \times 3 + 3) = 9$ ,

$x = 4 \Rightarrow y = (2 \times 4 + 3) = 11$ ,

$x = 5 \Rightarrow y = (2 \times 5 + 3) = 13$ ,

(i) $∴ f = {(2, 7), (3, 9), (4, 11), (5, 13)}$

(ii) Clearly, $dom (f) = {2, 3, 4, 5}$ and range (f) $= {7, 9, 11, 13} \subseteq Y$

(iii) It is clear that no two distinct ordered pairs in f have the same first coordinate.

$∴$ f is a function from X to Y.

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Let X={2,3,4,5} and Y={7,9,11,13,15,17}. Define a relation f from X to Y by: f={(x,y):xϵX, yϵY and y=2x+3} (i) Write f in roster form. (ii) Find dom(f) and range (f). (iii) Show that f is a function from X to Y.

Let $X = {2, 3, 4, 5}$ and $Y = {7, 9, 11, 13, 15, 17}$ . Define a relation f from X to Y by:
$f = {(x, y) : x ϵ X, y ϵ Y and y = 2 x + 3}$

(i) Write f in roster form.

(ii) Find dom(f) and range (f).

(iii) Show that f is a function from X to Y.