Question

For the functions (f(x) = -x² + 2x - 1) and (g(x) = x - 1), find (left(f/gright)(x)) and (left(f/gright)(1)).

A) (left(f/gright)(x) = -x + 3) and (left(f/gright)(1) = 4)
B) (left(f/gright)(x) = -x - 3) and (left(f/gright)(1) = -2)
C) (left(f/gright)(x) = -x - 1) and (left(f/gright)(1) = 0)
D) (left(f/gright)(x) = -x + 1) and (left(f/gright)(1) = 2)

Answer 1

To find (f/g)(x), we divide the function f(x) by the function g(x). The result is -x + 3. To find (f/g)(1), we substitute x = 1 into the expression and get 2.

Step-by-step explanation:

To find (f/g)(x), we need to divide the function f(x) by the function g(x). Let's divide each term of f(x) by g(x):

f(x)/g(x) = (-x² + 2x - 1)/(x - 1)

Now, let's simplify this expression by performing long division:

f(x)/g(x) = -x + 3

To find (f/g)(1), we substitute x = 1 into the expression we just found:

f(1)/g(1) = (-1 + 3) = 2