If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then

1.	If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find(i) f(-1)(ii) f(1/4 )(iii) f(-1.2)(iv) f(-6)
Answer» f(x) = 2{x} + 5x (i) {-1} = -1 – [-1] = -1 + 1 = 0 ∴ f(-1) = 2 {-1} + 5(-1) = 2(0) – 5 = -5 (ii) {1/4} = 1/4-0 = 1/4 f(1/4) = 2(1/4) + 5(1/4) = 2(1/4) + 5/4 = 7/4 = 1.75 (iii) {-1.2} = -1.2 – [-1.2] = -1.2 + 2 = 0.8 f(-1.2) = 2{-1.2} + 5(-1.2) = 2(0.8) + (-6) = -4.4 (iv) {-6} = -6 – [-6] = -6 + 6 = 0 f(-6) = 2{-6} + 5(-6) = 2(0) – 30 = -30

If f(x) = 2{x} + 5x, where {x} is fractional part function of x, then find(i) f(-1)(ii) f(1/4 )(iii) f(-1.2)(iv) f(-6)

Answer»

f(x) = 2{x} + 5x

(i) {-1} = -1 – [-1] = -1 + 1 = 0

∴ f(-1) = 2 {-1} + 5(-1)

= 2(0) – 5

= -5

(ii) {1/4} = 1/4-0 = 1/4

f(1/4) = 2(1/4) + 5(1/4)

= 2(1/4) + 5/4

= 7/4

= 1.75

(iii) {-1.2} = -1.2 – [-1.2] = -1.2 + 2 = 0.8

f(-1.2) = 2{-1.2} + 5(-1.2)

= 2(0.8) + (-6)

= -4.4

(iv) {-6} = -6 – [-6] = -6 + 6 = 0

f(-6) = 2{-6} + 5(-6)

= 2(0) – 30

= -30