Question

16. A function f : 6-7 6, h " R is defined as follows

Answer 1

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

SOLUTION :
(i) 2f(-4) +3 f(2)
For f(-4) :
Since -4 lies between -5 ≤ x ≤2 ,We take, f(x) = x + 5
f(-4) = -4 +5 = 1

For f(2): Since 2 lies between -5 ≤ x ≤2, We take, f(x) = x +5
f(2) = 2 + 5 = 7

Now , 2f(-4) +3 f(2) = 2(1) + 3(7) = 2 +21 = 23

Hence, the value of 2f(-4) +3 f(2)= 23

ii) f(-7) - f(-3)
For f(-7) :
Since -7 lies between -7≤ x < -5 ,We take, f(x) = x² + 2x +1
f(-7) = (-7)² + 2(-7) +1 = 49 -14 +1 = 35+1 = 36

For f(-3): Since -3 lies between -5 ≤ x ≤2, We take, f(x) = x +5
f(-3) = -3 +5 = 2

Now , f(-7) - f(-3) = 36 - 2 = 34

Hence, the value of f(-7) - f(-3) = 34

iii) 4f(-3) + 2f(4) / f(-6) - 3f(1).
For f(1) & f(3)
Since 1 & 3 lies between -5 ≤ x ≤2, We take, f(x) = x +5
f(1) = 1 +5 = 6
f(-3) = -3 +5 = 2

For f(4): Since 4 lies between 2 < x < 6 We take, f(x) = x -1
f(4) = 4 -1= 3

For f(-6): Since -6 lies between -7≤ x < -5 ,We take, f(x) = x² + 2x +1
f(-6) = (-6)² +2(-6) +1 = 36 -12 +1= 24 +1 = 25

Now , 4f(-3) + 2f(4) / f(-6) - 3f(1) = 4(2) +2(3) / 25 - 3(6)
= 8 +6 / 25 -18
= 14 /7 = 2

Hence, the value of 4f(-3) + 2f(4) / f(-6) - 3f(1) = 2

HOPE THIS WILL HELP YOU..