# Functions: Inverses and Composite Functions

The problems are all in multiple choice format so pick the most correct answer in each case and show your work.

The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients.

a. f(x) = (x + 3)(x^2 + 16)

b. f(x) = (x + 3)(x^2 + 8x + 16)

c. f(x) = (x + 3)(x^2 - 8x + 16)

d. f(x) = (x - 3)(x^2 + 16)

Find the inverse of the function f(x) = x^(1/3) + 2.

a. (x - 2)^3

b. x^(1/3) + 2

c. (y - 2)^3

d. Doesn't exist

From the information in the table providing values of f(x) and g(x) evaluate (f o g)^-1(2).

x 1 2 3 4 5

f(x) 3 4 5 1 2

g(x) 5 4 2 3 1

a. 1

b. 2

c. 4

d. 5

A bacteria culture started with a count of 720 at 8:00 A.M., and after t hours is expected to grow to f(t) = 720(3/2)^t. Estimate the number of bacteria in the culture at 11:00 A.M. the same day.

a. 1620

b. 2160

c. 2430

d. 2880

https://brainmass.com/math/complex-analysis/functions-inverses-and-composite-functions-130117

#### Solution Summary

This solution illustrates how to solve for inverses and composite functions. The response is enclosed within an attached Word document.