Answer:
(0,2) is the solution of the given functions.
Step-by-step explanation:
We have been given two functions f(x)=|x-1|+1 and g(x)=3x+2
To find the solution of the two functions mathematically, we will equate the given functions:
3x+2=|x-1|+1
3x+1=|x-1|
When we will open the modulus function we will have two values +, -
In positive case:
3x+1 =x-1
2x=-2
x=-1
Now, substitute x=-1 in g(x)=3x+2 we get
g(-1)=3(-1)+2=-1
Hence, (-1,-1) is the solution of the given functions.
In negative case:
Now, 3x+1=-(x-1)
3x+1=-x+1
4x=0
x=0
Now, put x=0 in g(x)=3x+2 we get
g(0)=3(0)+2=2
We have another solution: (0,2)
The point (2,2) is not the solution.
And graphically, the solution of two functions is their intersection point which is (0,2)
Hence, (0,2) is the solution of the function.
