Question

a function f :[-3,7] ris 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))

Answer 1

Answer:

(i). 16 ; (ii). - 4 ; (iii). 5 ; (iv). 2(8/15)

Step-by-step explanation:

f(x) = {4x² – 1, if -3 ≤ x < 2} ..... (1)

f(x) = {3x – 2, if 2 ≤ x ≤ 4} ...... (2)

f(x) = {2x – 3, if 4 < x < 7} ...... (3)

(i). f(5) + f(6) , 5 ∈ (3) and 6 ∈ (3)

2 × 5 - 3 + 2 × 6 - 3 = 7 + 9 = 16

f(5) + f(6) = 16

(ii). f(1) - f(3) , 1 ∈ (1) , 3 ∈ (2) ,

Thus, f(1) = 4(1)² - 1 = 3 and f(3) = 3×3 - 2 = 7 ⇒ f(1) - f(3) = 3 - 7 = - 4

(iii). f(- 2) - f(4) , - 2 ∈ (1) , 4 ∈ (2) ,

f(- 2) = 4(- 2)² - 1 = 15 and f(4) = 3×4 - 2 = 10 ⇒ f(- 2) - f(4) = 15 - 10 = 5

(iv). $\frac{f(-3)+f(-1)}{2f(6)-f(1)}$ , Numerator ∈ (1) , Denominator ∈ (3) and (1)

f(- 3) = 4(- 3)² - 1 = 35 and f(- 1) = 4(- 1)² - 1 = 3 ⇒ Numerator = 35 + 3 = 38

2f(6) = 2(2×6 - 3) = 18 and f(1) = 3 ⇒ Denominator = 18 - 3 = 15

$\frac{Numerator}{Denominator}$ = 38 ÷ 15 = $2\frac{8}{15}$