Consider the following functions. (c) f: GL₂(R) → RX, f + ((ad)) (($)) (d) f: GL₂(R) → R, ƒ (e) f: GL₂(R) → RX, f = ab. = a + d. (i) Is f a homomorphism? (ii) Is f injective? = ad-bc. For each of these functions, answer the following questions, with a (brief) justifi- cation.

I came up with the example 1/x + 1/x - 2. Can you prove this is injective by contrapositive as well as proving that it is surjective?

Let us define a number a to be a fixed point of a function f if a = f(a). (For example, if f (x) = -x², then x = -1 is a fixed point because f(–1) = -1.) Prove that if f'(x) # 1 for all numbers x, then f has at most one fixed point.

2. The function f(x) is defined by the table shown below: Fill in the blanks: (a) f(_ I T(2) -3 -2 -1 0 1 2 0 1 2 345 (b) f(0) = =0 (c) f(2)= (d) f( ) = 1