Got class in 30 mins, 3 problems I dont know how to solve

Quote:

Originally Posted by mwok

These are incredibly difficult

2) A fourth degree polynomial f(x) with real coefficients and leading coefficient of 1 has zeroes of -1, 2,1 -i. Write the polynomial as a product of linear and quadratic factors with real coefficients that are irreducible over R (this R represents the real number like I think)

Mr F says: If the coefficients are real then 1 + i is also a root. Then the polynomial can be written f(x) = (x + 1)(x - 2)(x - 1 + i)(x - 1 - i). The last two factors expand to give (x - 1)^2 + 1 = ......

2) Find values a,b, and c for exponential function f(x) = cb^-x + a. Given that the horizontal asymptote is y = 72. Y intercept is 425 and point P (1,248.5) lies on the graph.

Mr F says: You should know that according to the model the horizontal asymptote is y = a. Therefore a = 72.

Substitute (0, 425) and (1, 248.5) into ${\color{red}f(x) = c b^{-x} + 72}$ to get two equations in c and b. Solve these two equations simultaneously.

I did y=mx + b and got M=176.5 but what about the rest (c,b,a,x)?

3) Determine the domain and range of f^1 for the function f(x) = (4x+5)/(3x-8), without actually finding f^1

Mr F says: dom f = ran f^-1 and ran f = dom f^-1. Note also that ${\color{red}f(x) = \frac{47}{3(3x-8)} + \frac{4}{3}}$

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