Question

Let ​ f(x)=x+2 ​ and ​ g(x)=align="absmiddle" class="latex-formula">+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

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