Question

The function f(x) = g(x), where f(x) = 2x - 5 and g(x) = x2 - 6.

Answer 1

Answer:

• The positive solution to the nearest tenth is (2.4, - 0.2).

Explanation:

I will rewrite the table to understand how the process of solving using succesive approximations is.

Table:

x        f(x)      g(x)

0        - 5      - 6

1         - 3       - 5

2        - 1       - 2

3          1          3

Those are the points shown in the table.

Now you must continue the process of solving using successive approximations until you find the positive solution to the nearest tenth.

You need to determine whether a "guess" is closer or farther away of the solution.

The first row shows that g(x) is less than f(x) in 1 unit when x = 0 ( -6 - (-5) ) = -1.

The second raw shows that g(x) is less than g(x) in 2 units when x = 1 ( - 5 - (-3) ) = - 2

The third row shows that g(x) is is less than f(x) in 1 unit when x = 2 ( - 2 - (-1) ) = - 1.

The fourth row shows that g(x) is than f(x) in 2 units when x = 3 ( 3 - 1 = 2).

Hence, the trend changed form negative to positive, meaning that, since the functions are continous, there must be an intertemediate value of x (between x = 2 and x = 3) for which f(x) = g(x) and that is the solution.

Therefore, test x = 2.5

• f(x) = 2x - 5 = 2(2.5) - 5 = 0
• g(x) = x² - 6 = (2.5)² - 6 = 0.25

• g(x) - f(x) = 0.25 Thus the difference is bigger than one tenth (0.1)

Test for x = 2.4

• f(2.4) = 2(2.4) - 5 = - 0.2
• g(2.4) = 2.4² - 6 = -0.24

• g(2.4) - f(2.4) = - 0.24 - (0.2) = -0.04

Now the difference is less than 0.1 and the solution to the nearest tenth is (2.4, - 0.2).