1. Recall the definition of injection, surjection, and bijection given in Chapter 10. Establish which ones of the following functions are injections, surjections, and bijections. In case a function is not an injection, or not a surjection, or not a bijection, explain why. (a) f: {0, 1,2,3} → {♡,} such that ƒ(0) = f(1) = f(3) = ♡ and ƒ(2) = (b) g: {0, 1, 2, 3} → {0, 1, 4, 9} such that g(n) = n². (c) h: N→ N such that h(n) (d) k: Z→ N such that k(n) = |n|, the absolute value function. = n + 1.

Just need help with Questions D and E. Thank you so much.

3. not. Is the function f: R → R defined by is f(x) = x² + 3x – 2 injective? Show clearly why or why

Find the critical point for the function: a* /5 – a/4+ 1/3 1+ (æ³/5 – æ/4 +1/3)2 | for xe[-1,1]. Which of these critical points are local maxima?

5. Let f(x) = 2x and g(x) = x² be functions in PC[−2,2]. a. Find (f, g) b. Find ||f|| c. Find ||g||

1. Let f(x) = 12 + 22 + 32 + ..+x². Show f(x) is 0(x³).

Suppose that z is a differentiable function of s, t, u, and v. Also suppose that s, t, u, and v are differentiable functions of x and y. Write the chain rule formula for дz/дх.

10. Let Is f convex, concave, or neither? f(x₁,1₂)=x²-x₁x₂ + x² + 3x₁2x2 +1 (x₁; ₂) € R².