Let f: R → R such that f (x) = x ^ 2 Analyze if the function is continuous by taking the domain and the codomain with the following topologies: a) τ1 = {R, ∅, (0, 1)} b) τ2 = {R, ∅, {(a, ∞) | a ∈ R}}

Let T: R³ R2 be a linear mapping. → 10 *([:]) = [ ] ¹ ({]) - [ ] -~-~(:)) - [²7] ([]) - T = and T find T (ED). Given that T sin (a) Ər f α Ω E

Let f : (−1,1) → R, f(x) = (1 + x³) -³. Compute g' : (0, 1) → R where X (a) g(x) = f * ƒ f. (b) g(x) = [* x f.

5. Consider the function f! NXN → N, defined by f(m,n) = min +1 a) find f(A)= A= {(1,0), (0, 1), (1,1) 3 b) find pre-image of B = {0,13 by f 1.e., F-1 (B) := f `¹ (0) U f `` (1) c) Is f an injective (or one-to-one) function.? Justify answer. d) Is f a surjective (or onto) function. Justify answer.