Question

Let f(x) = |x − 2| + 1 and g(x) = 1/3 x + 3. When does f(x) = g(x)?

Answer 1

x=0 and x=6

Explanation:

First, we need to set these two functions equal to each other and then we need to solve for x.

`|x-2|+1=(1)/(3) x+3\\\\|x-2|=(1)/(3)x+2`

To get rid of the absolute values, we have to add both a + and a - to the other side. This will split the equation into two different equations. Lets solve for the + side first.

`x-2=(1)/(3)x+2\\\\x=(1)/(3)x+4\\\\(2)/(3)x=4\\\\x=(12)/(2) =6\\\\x=6`

And now for the - side.

`x-2=-(1)/(3)x-2\\\\x=-(1)/(3)x\\\\x=0`