Question

Write the values of f at − 4, 1, −2, 7, 0 if

f(x) = `{{:(- x + 4,  "if" - ∞ < x ≤ - 3),(x + 4,  "if" - 3 < x < -2),(x^2 - x,  "if" - 2 ≤ x < 1),(x - x^2,  "if"  1 ≤ x < 7),(0,  "otherwise"):}`

Answer 1

f(x) = `{{:(- x + 4,  "if" - ∞ < x ≤ - 3),(x + 4,  "if" - 3 < x < -2),(x^2 - x,  "if" - 2 ≤ x < 1),(x - x^2,  "if"  1 ≤ x < 7),(0,  "otherwise"):}`

When x = − 4

f(x) = – x + 4

f(−4) = – (− 4) + 4

= 4 + 4

= 8

When x = 1

f(x) = x – x²

f(1) = 1 – 1²

= 1 – 1

= 0

When x = −2

f(x) = x² – x

f(−2) = (−2)² – (−2)

= 4 + 2

= 6

When x – 7

f(x) = 0

⇒ f(7) = 0

When x = 0

f(x) = x² – x

⇒ f(0) = 0² – 0

= 0