Question

Glven the system below:

f(x) = 2^x
g(x) = 2^x
Which value(s) of x make f(x) = g(x) a true statement? If necessary, you may choose more than one answer.

Answer 1

The correct answers are 1 and 2.

Given the functions, f(x) = 2x and g(x) = 2^x

Plug the given options to see which value of x makes f(x) = g(x):

For x = 0:

f(0) = 2(0) = 0
g(0) = 2^(0) = 1

Therefore, since f(0) ≠ g(0), then it is not a solution to the given system.


For x = 1:

f( 1 ) = 2( 1 ) = 2
g( 1 )= 2^( 1 ) = 2

Therefore, since f(1 ) = g( 1 ), then IT IS a solution to the given system.

For x = 2

f( 2 ) = 2( 2 ) = 4
g( 2 )= 2^( 2 ) = 4

Therefore, since f( 2 ) = g( 2 ), then IT IS a solution to the given system.

For x = 3:

f(3) = 2(3) = 6
g(3) = 2^(3) = 8

Therefore, since f(3) ≠ g(3), then it is not a solution to the given system.

For x = 4:

f(4) = 2(4) = 8
g(4) = 2^(4) = 16

Therefore, since f(4) ≠ g(4), then it is not a solution to the given system.


Thus, 1 and 2 are the solutions to the given system that makes f(x) = g(x).