University:
Carleton College
Course:
MATH 101 | Calculus with Problem Solving
Academic year:

2024
Views:

224

Pages:

2
Author:

larbiwxcvbn

Even, Odd, One-to-One, Inverse Functions WS Name: Hour: Pre-Calculus The graph of a function defined for x ≥ 0 is given. Complete the graph for x < 0 to make a) an even function and b) an odd function. a. EVEN even function graph b. ODD odd function graph a. EVEN even function graph b. ODD odd function graph Determine whether the function is even, odd, or neither. f(x) = x² + x f(-x) = (-x)² + (-x) = x² - x NEITHER f(x) = x³ - x f(-x) = (-x)³ - (-x) = -x³ + x ODD f(x) = -1 - 1/√x f(-x) = -1 - 1/√(-x) = -1 - i/√x NEITHER f(x) = x⁴ + x² + 2 f(-x) = (-x)⁴ + (-x)² + 2 = x⁴ + x² + 2 EVEN Determine whether the function is one-to-one. f(x) = -x + 6 ONE TO ONE f(x) = x² - 5x NOT ONE TO ONE parabola f(x) = √x ONE TO ONE f(x) = |x + 2| NOT ONE TO ONE absolute value function f(x) = x³ - 2x + 5NOT ONE TO ONE cubic function f(x) = √(4 - x²)NOT ONE TO ONE semicircle Find the Inverse of the Function. 13. f(x) = 4x + 7 y = 4x + 7 x = 4y + 7 x - 7 = 4y (x - 7) / 4 = y f⁻¹(x) = (x - 7) / 4 14. f(x) = 5 - 4x³ y = 5 - 4x³ x = 5 - 4y³ x - 5 = -4y³ (x - 5) / -4 = y³ ∛((5 - x) / -4) = y = f⁻¹(x) 15. f(x) = √(5x - 7) y = √(5x - 7) x = √(5y - 7) x² = 5y - 7 x² + 7 = 5y (x² + 7) / 5 = y = f⁻¹(x) 16. f(x) = 6 + ∛(x + 1) y = 6 + ∛(x + 1) x = 6 + ∛(y + 1) x - 6 = ∛(y + 1) (x - 6)³ = y + 1 (x - 6)³ - 1 = y f⁻¹(x) = (x - 6)³ - 1 17. f(x) = 1 / (x + 2) y = 1 / (x + 2) x = 1 / (y + 2) x(y + 2) = 1 xy + 2x = 1 y + 2 = 1/x y = 1/x - 2 f⁻¹(x) = 1/x - 2 or f⁻¹(x) = (1 - 2x) / x 18. f(x) = 4 - x², x ≥ 0 y = 4 - x² x = 4 - y² x - 4 = -y² 4 - x = y² √(4 - x) = y f⁻¹(x) = √(4 - x)