If f(x) = 4[x] – 3, where [x] is greatest integer function of x, the

1.	If f(x) = 4[x] – 3, where [x] is greatest integer function of x, then find(i) f(7.2)(ii) f(0.5)(iii) f(-5/2)(iv) f(2π), where π = 3.14
Answer» f(x) = 4[x] – 3 (i) f(7.2) = 4 [7.2] – 3 = 4(7) – 3 ………[∵ 7 ≤ 7.2 < 8, [7.2] = 7] = 25 (ii) f(0.5) = 4[0.5] – 3 = 4(0) – 3 ………[∵ 0 ≤ 0.5 < 1, [0.5] = 0] = -3 (iii) f(-5/2) = f(-2.5) = 4[-2.5] – 3 = 4(-3) – 3 …….[∵-3 ≤ -2.5 ≤ -2, [-2.5] = -3] = -15 (iv) f(2π) = 4[2π] – 3 = 4[6.28] – 3 …..[∵ π = 3.14] = 4(6) – 3 …….[∵ 6 ≤ 6.28 < 7, [6.28] = 6] = 21

If f(x) = 4[x] – 3, where [x] is greatest integer function of x, then find(i) f(7.2)(ii) f(0.5)(iii) f(-5/2)(iv) f(2π), where π = 3.14

Answer»

f(x) = 4[x] – 3

(i) f(7.2) = 4 [7.2] – 3

= 4(7) – 3 ………[∵ 7 ≤ 7.2 < 8, [7.2] = 7]

= 25

(ii) f(0.5) = 4[0.5] – 3 = 4(0) – 3 ………[∵ 0 ≤ 0.5 < 1, [0.5] = 0]

= -3

(iii) f(-5/2) = f(-2.5)

= 4[-2.5] – 3

= 4(-3) – 3 …….[∵-3 ≤ -2.5 ≤ -2, [-2.5] = -3]

= -15

(iv) f(2π) = 4[2π] – 3

= 4[6.28] – 3 …..[∵ π = 3.14]

= 4(6) – 3 …….[∵ 6 ≤ 6.28 < 7, [6.28] = 6]

= 21