Question

Let f : R → R be defined by 

f(x) = `{(3x;    x > 2),(2x^2;    1 ≤ x ≤ 2), (4x;   x < 1):}`

Then f(-2) + f(1) + f(3) is ______ 

Options

• 3

• 19

• 5

• 10

Answer 1

Let f : R → R be defined by 

f(x) = `{(3x;    x > 2),(2x^2;    1 ≤ x ≤ 2), (4x;   x < 1):}`

Then f(-2) + f(1) + f(3) is 3.

Explanation:

f(x) = `{(3x;    x > 2),(2x^2;    1 ≤ x ≤ 2), (4x;   x < 1):}`

∴ as, x = -2, f(x) = f(-2) = 4(-2) = -8

as, x = 1, f(x) = f(1) = 2(1)² = 2

as, x = 3, f(x) = f(3) = 3(3) = 9

∴ f(-2) + f(1) + f(3) = 3