Question

15. A function f : 6-3 7, h " R is defined as follows
f x^ h = Find

Answer 1

QUESTION :
A function f : [-3, 7) → R is defined as follows.
f (x) = 4x²-1; -3 ≤ x <2
3x -2 ; 2 ≤ x ≤4
2x -3 ; 4 < x < 7
Find (i)f(5) + f(6) (ii) f(1) - f(-3)
(iii) f(-2) - f(4) (iv) f(3) + f(-1) / 2f(6) - f(1).

SOLUTION :
(i)
For f(5) :
Since 5 lies between 4 and 7 ,We take, f(x) = 2x -3
f(5) = 2×5 -3 = 10 -3 = 7

For f(6): Since 6 lies between 4 and 7 , We take, f(x) = 2x -3
f(6) = 2×6 -3 = 12 -3 = 9

Now , f(5) + f(6) = 7 +9 = 16

Hence, the value of f(5) + f(6) = 16

ii)
For f(1) :
Since 1 lies between -3 and 2 , We take , f(x) = 4x² -1
f(1) = 4(1)² -1 = 4 -1= 3

For f(-3): Since -3 lies between -3 and 2, We take, f(x) = 4x² -1
f(-3) = 4(-3)² -1 = 4 ×9 -1 = 36 -1= 35

Now , f(1) - f(-3) = 3 -(35) = -32

Hence, the value of f(1) - f(-3) = -32

iii)
For f(-2) :
Since 1 lies between -3 and 2 ,We take , f(x) = 4x² -1
f(-2) = 4(-2)² -1 = 4×4 -1 = 16 -1= 15

For f(4): Since 4 lies between 2 and 4, We take, f(x) = 3x -2
f(4) = 3×4 -2 = 12 -2 = 10

Now , f(-2) - f(4) = 15 - 10= 5

Hence, the value of f(-2) - f(4) = 5

iv)
For f(3) :
Since 3 lies between 2 and 4 , We take , f(x) = 3x -2
f(3) = 3×3 -2 = 9 -2 = 7

For f(-1): Since -1 lies between -3 and 2, We take, f(x) = 4x² -1
f(-1) = 4(-1)² -1 = 4 -1 = 3

For f(6) : Since 6 lies between 4 and 6, We take, f(x) = 2x -3
f(6) = 2×6 -3 = 12 -3 = 9

For f(1) :
Since 1 lies between -3 and 2 , We take , f(x) = 4x² -1
f(1) = 4(1)² -1 = 4 -1= 3

Now , f(3) + f(-1) / 2f(6) - f(1) =( 7 + 3) /2(9) - 3
= 10/ (18-3) = 10 / 15 = 2/3

Hence, the value of f(3) + f(-1) / 2f(6) - f(1) = 2/3

HOPE THIS WILL HELP YOU...