Question

MATHEMATICS-XI
3.8
8. Write the following relations as sets of ordered pairs and find which of them are functions:
(i) {(x, y): y = 3x, x = (1, 2, 3), y e{3,6,9,12}}.
(ii) {(x, y): y > x+1, x =1, 2 and y = 2, 4, 6) (iii) {(x, y): x + y = 3, x, y € {0, 1, 2, 3}}
9. Let f: RR and g:
CC be two functions defined as f (x) = x2 and g(x) = x2. Are they
equal functions?
10. If f, g, h are three functions defined from R to R as follows:
(i) f (x) = x2
(ii) g(x) = sin * (iii) h(x) = x2 + 1
Find the range of each function.
11. Let X = {1, 2, 3, 4 and Y = (1,5,9, 11, 15, 16)
Determine which of the following sets are functions from X to Y
Gif
1/11 (7)

Answer 1

Step-by-step explanation:

1. Twice the rational number -7/3 is 2*(-7/3)=-14/3 suppose x added to this number gives 3/7
2. x +(-14/3)=3/7
3. x-14/3=3/7
4. x=3/7+14/3
5. (3*3)+(14*7)/21 =9+98/21=107/21
6. Thus 107/21 should be added to 2*(-7/3) to give 3/7

Answer 2

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Given function:

f(x) = x2 − 3x + 2.

To find f(f(x))

f(f(x)) = f(x)√2 − 3f(x) + 2.

= (x^2 – 3x + 2)^2 – 3(x^2 – 3x + 2) + 2

By using the formula (a-b+c)2 = a2+ b2+ c2-2ab +2ac-2ab, we get

= (x^2)^2 + (3x)^2 + 22– 2x^2 (3x) + 2x^2(2) – 2x^2(3x) – 3(x^2 – 3x + 2) + 2

Now, substitute the values

= x^4 + 9x^2 + 4 – 6x^3 – 12x + 4x^2 – 3x^2 + 9x – 6 + 2

= x^4 – 6x^3 + 9x^2 + 4x^2 – 3x^2 – 12x + 9x – 6 + 2 + 4

Simplify the expression, we get,

f(f(x)) = x^4 – 6x^3 + 10x^2 – 3x

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Hope It's Helpful.....:)