Question

Write the values of f at −3, 5, 2, −1, 0 if

f(x) = `{{:(x^2 + x - 5,  "if"  x ∈ (−∞, 0)),(x^2 + 3x - 2,  "if"  x ∈ (3, ∞)),(x^2,  "if"  x ∈ (0",", 2)),(x^2 - 3,  "otherwise"):}`

Answer 1

f(x) = `{{:(x^2 + x - 5,  "if"  x ∈ (−∞, 0)),(x^2 + 3x - 2,  "if"  x ∈ (3, ∞)),(x^2,  "if"  x ∈ (0",", 2)),(x^2 - 3,  "otherwise"):}`

When x = – 3

f(x) = x² + x – 5

f(– 3) = (– 3)² + (– 3) – 5

= 9 – 3 – 5

= 9 – 8

= 1

When x = 5

f(x) = x² + 3x – 2

f(5) = 5² + 3(5) – 2

= 25 + 15 – 2

= 40 – 2

= 38

When x = 2

f(x) = x² – 3

f(2) = 2² – 3

= 4 – 3

= 1

When x = – 1

f(x) = x² + x – 5

f(–1) = (–1)² – 1 – 5

= 1 – 1 – 5

= – 5

When x = 0

f(x) = x² – 3

f(0) = 0² – 3