1:33 Math 90+90S Climax 2... Math 90+90S Climax 2 Show all work. Use only real numbers. 0. What are your (L) last and (F) first names? 0.(L) 1. [20] Please find the domain of f. f(x) = x²-2x-3 x-1 1. (F) 4+ 2. [15] Let P(x) = x² - 4x³ +12x-9. Please use the Rational Root Theorem and the Synthetic Division Theorem to factor P(x) completely. (Linear factors only, please.) 2. 3. [25] Please sketch the graph of each. Label all important features. Find the requested values of g. (a) f(x) = x²+4 (b) g(x) = {1 if x <2 if x ≥ 2 g(√5)= g(√3) = 4. [20] Suppose f(x) = 2√√x +4. (a) Please sketch the graph of ƒ in the space below without plotting points. Label the intercepts. (b) Please find and simplify f-1(x). 4.(a) 4.(b) 1/n3. [25] Please sketch the graph of each. Label all important features. Find the requested values of g. (a) f(x) = x²-4 x+1 (b) g(x) = {1 if x <2 if x ≥ 2 g(√5)= g(√3) 4. [20] Suppose f(x) = 2-√√x +4. (a) Please sketch the graph of ƒ in the space below without plotting points. Label the intercepts. (b) Please find and simplify f-1(x). 4.(a) 4.(b) 5. [10] Please prove that fis one-to-one, where f(x) = 3x² + 12x-1 (x ≤ -2). 6. [10] One of these graphs represents an invertible function f; the other does not. Choose the invertible function and sketch the graph of f-1 in the space to the right. Label all important features. Ly 5- +2 2 of 2

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