Question

Let f: R → R be defined by f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`. Then f(–1) + f(2) + f(4) is ______.

विकल्प

• 9

• 14

• 5

• None of these

Answer 1

Let f: R → R be defined by f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`. Then f(–1) + f(2) + f(4) is 9.

Explanation:

Given that, f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`

f(–1) = 3(–1) = –3  .....(Using f(x) = 3x)

f(2)= 2² = 4  ......(Using f(x) = x²)

f(4) = 2(4) = 8  ......(Using f(x) = 2x)

∴ f(–1) + f(2) + f(4) = 3 + 4 + 8 = 9