Question

Select the correct answer. Consider functions f and g. fx=x4-16x3+94x2-240x+225 gx= 1/x-4 -1

Using graphing, what is the solution, or solutions, of fx=gx x=5 x=0;x=3 x=0;x=5 x=3

A) x = 5
B) x = 0 ; x = 3
C) x = 0 ; x = 5
D) x = 3

Answer 1

To solve f(x) = g(x), set the given polynomial and rational functions equal to each other and simplify to find a common solution. Without full details or sufficient simplification, we cannot accurately determine the solutions, though graphing can help identify where the functions intersect.

Step-by-step explanation:

Solving the Equation f(x) = g(x)

To solve the equation where f(x) equals g(x), we must set the two functions equal to each other and simplify.

The function f(x) is given by f(x) = x4 - 16x3 + 94x2 - 240x + 225, and g(x) is given by g(x) = 1/(x-4) - 1. Setting them equal gives us the equation x4 - 16x3 + 94x2 - 240x + 225 = 1/(x-4) - 1. Simplifying the right side by finding a common denominator and subtracting 1 leads us to a polynomial equation. This polynomial equation can then be factored or solved using the quadratic formula if it is indeed a quadratic equation. However, without sufficient information or the full simplification of the original equation, we cannot proceed to find the solution accurately. Therefore, more clarification or steps are needed to solve this problem.

Graphing the functions to find the intersection points would also show us the solutions. We are looking for the x-values where the two graphs intersect, which would be the values for x where f(x) and g(x) are equal.