Let ​ f(x)=x+2 ​ and ​ g(x)=2^(x)+1 ​ . Graph the functions on the same coordinate plane. What are the solutions to the equation f(x)=g(x) ? Enter your answers in the boxes. x =…

Question

Let ​ f(x)=x+2 ​ and ​ g(x)=
`2^(x)`+1 ​ .

Graph the functions on the same coordinate plane.


What are the solutions to the equation f(x)=g(x) ?



Enter your answers in the boxes.

x = ___ or x = ____

Answer 1

Answer: x = 0 and x = 1

Step-by-step explanation:

The image of the graph is in the figure attached.

There you can observe two intersection points which are (0,2) and (1,3), therefore the solutions are x = 0 and x = 1.

You can draw the graph by constructing a table with x from - 2 to 4, like this:

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

-2 -2 + 2 = 0 2^2 + 1 = 4 + 1 = 5

- 1 -1 + 2 = 1 2^1 + 1 = 2 + 1 = 3

0 0 + 2 = 2 2^0 + 1 = 1 + 1 = 2 => this is one solution

1 1+ 2 = 3 2^1 + 1 = 2 + 1 = 3 => this is the other solution

2 2 + 2 = 4 2^2 + 1 = 4 + 1 = 5