Question

Graph f(x)=3x-1 and g(x)=2^x on the same coordinate plane.

What are the solutions of 3x-1=2^x?

A. -1
B. 1
C. 8
D. 3
E. 0

Answer 1

B. 1 and D. 3.

Explanation:

The figure below shows the graphs of f(x) = 3x - 1 (red) and g(x) = 2^x (blue).

The solutions of 3x - 1 = 2^x are the points at which the two curves intersect.

The solutions are at x = 1 and x = 3.

Check:

3 × 1 - 1 = 2¹ 3 × 3 -1 = 2³

3 - 1 = 2 9 - 1 = 8

2 = 2 8 = 8