How do you do these problems Problem 1all a ER.commutes with f(x). Find e in terms of m.A Show that for m 1, the functions f and g in (a) have the samefixed points.e Ceneralise (b) as follows: for arbitrary functions f,g: R R, provethat if f and g commute and f has a unique fixed point To, then ois also a fixed point of g.Problem 2Consider a cubic function f : R → IR where f(x) = x³ + bx2 + cx + d.(a) Explain why f is surjective.(b) Show that f (x) can also be written in the form g(X) = X3 +CX+D,%3Dwhere C = c-5. Find an expression for D in terms of b, c and d.(c) Given that f is injective, show that 3c > 6².Problem 3Given non-zero integers a, b and c, let a and B be the solutions of thegeneral quadratic equation ax?+ bx +c= 0.(a) Find a quadratic equation with integer coefficients whose solutionsare+1 and -+ 1.(b) Under what conditions on a, b and c will the new equation have thesame pair of solutions as the original equation?Problem 4Solve the following system of equations.1- + - + - =1x²yz + xy°z + xyz? = -4zy(x + y) + yz(y + z) + zæ(z + x) = 4

Name: How do you do these problems Problem 1all a ER.commutes with f(x). Fin
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: How do you do these problems Problem 1all a ER.commutes with f(x). Find e in terms of m.A Show that for m 1, the functions f and g in (a) have the samefixed points.e Ceneralise (b) as follows: for arbitrary functions f,g: R R, provethat if f and g co