Question

The functions f(x)=−3/4x+2 1/4 and g(x)=(1/2)^x+1 are shown in the graph.

What are the solutions to −3/4x+2 1/4=(1/2^)x+1?

Select each correct answer.




−1

0

1

2

3

Answer 1

-3x/4 + 9/4 = (1/2)^x + 1
-3x/4 - 2^-x = -5/4

(Using log rules)

㏑|-3x/4| - ㏑|2^-x| = ㏑|-5/4|
㏑|3x/4| - x㏑|2| = ㏑|5/4|
e^㏑|3x/4| - e^㏑|2|x = e^㏑|5/4|
|3x/4| - 2x = 5/4
|3x| - 8x = 5
|3x-8x| = 5
|-5x| = 5
|5x| = 5
x=1, -1