Question

The table below shows some values of f(x) and g(x) for different values of x:

x f(x) = 2x + 24 g(x) = 5(0.5)x
−2 20
−1
0 5
1 2.5
2 28
Complete the chart and determine the solution of the equation f(x) = g(x). (5 points)


x = −2
x = −1
x = 1
x = 20

Answer 1

The correct answer to this question is answer A (x = −2)

I just took the test.

Answer 2

The first thing we must do for this case is to complete the table.
We have then:
For f (x) = 2x + 24:
f (-2) = 2 (-2) + 24 = 20
f (-1) = 2 (-1) + 24 = 22
f (0) = 2 (0) + 24 = 24
f (1) = 2 (1) + 24 = 26
f (2) = 2 (2) + 24 = 28


For g (x) = 5 (0.5) ^ x:
g (-2) = 5 (0.5) ^ - 2 = 20
g (-1) = 5 (0.5) ^ - 1 = 10
g (0) = 5 (0.5) ^ 0 = 5
g (1) = 5 (0.5) ^ 1 = 2.5
g (2) = 5 (0.5) ^ 2 = 1.25
The table is:
x f(x) g(x)
-2 20 20
-1 22 10
0 24 5
1 26 2.5
2 28 1.25
f (x) = g (x) occurs for:
x = -2

Answer:
-2 20 20
-1 22 10
0 24 5
1 26 2.5
2 28 1.25
f (x) = g (x) ----> x = -2