Question

Consider functions fand g.

f(x)= log (x-1)
g(x)= 1/2x2 - 4
Which statement gives the best approximation of the solutions of the equation f(x) = g(x)?
=
OA.
The solutions are where the graphs of the functions cross the x-axis at ≈ -3.464and ≈ 3.642.
OB. The solutions are where the graphs of the functions intersect at
-3.464and ≈ 3.464.
OC. The solutions are where the graphs of the functions intersect at
land ≈ 3.642.
OD. The solutions are where the graphs of the functions cross the x-axis at ≈ -4and ≈ 0.422.
d

Answer 1

The best approximation of the solutions of the equation f(x) = g(x) can be found by finding the x-values where the graphs of the functions f(x) and g(x) intersect. Using a graphing calculator or software, the approximate solutions are x = -3.464 and x = 3.642.

Step-by-step explanation:

The best approximation of the solutions of the equation f(x) = g(x) can be found by finding the x-values where the graphs of the functions f(x) and g(x) intersect.

To find the intersection points, set f(x) equal to g(x) and solve for x:

log(x-1) = 1/2x^2 - 4

Since it is not possible to solve this equation algebraically, we can use a graphing calculator or software to find the approximate solutions. For this equation, the solutions are approximately x = -3.464 and x = 3.642.

Therefore, the statement that gives the best approximation of the solutions of the equation f(x) = g(x) is option OA: The solutions are where the graphs of the functions cross the x-axis at ≈ -3.464 and ≈ 3.642.