The absolute value transforms a negative number into a positive number.
For example
Let z be a real number, then:
| z | It will always be a positive number.
This means that:
If z is a negative number, then:
| z | = -z
If z is a positive number, then:
| z | = z
This means that for the expression the expression y = 2 | x-3 | +5
When x-3 > 0 then:
| x-3 | = x-3
When x-3 < 0 then:
| x-3 | = - (x-3)
Then we can divide the expression into two functions f (x) and g (x).
f (x) = 2 (x-3) +5
f (x) = 2x-6 + 5
f (x) = 2x-1
For
[tex](x-3) \geq 0\\ x \geq 3[/tex]
g (x) = 2 (-x + 3) +5
g (x) = -2x + 6 + 5
g (x) -2x +11
For
(x-3) < 0
x < 3
Answer:
The two functions are [tex]f(x)=-2x+6,\; x<3\;\&\;g(x)=2x-1,\; x>3.[/tex]
Step-by-step explanation:
Given: the equation [tex]y=2\mid{x-3}\mid+5[/tex].
From the question,
If [tex](x-3)<0[/tex], then [tex]\mid{x-3}\mid=-(x-3)[/tex]
If [tex](x-3)>0[/tex], then [tex]\mid{x-3}\mid=(x-3)[/tex]
Now, divide the given expression into two different functions [tex]f(x)\; \&\; g(x)[/tex] and solve it further
Here, [tex](x-3)<0[/tex] then [tex]f(x)=-2(x-3)+5[/tex]
[tex]f(x)=-2(x-3)+5\\f(x)=-2x+6+5\\f(x)=-2x+6[/tex]
And, [tex](x-3)>0[/tex] then [tex]g(x)=2(x-3)+5[/tex]
[tex]g(x)=2(x-3)+5\\g(x)=2x-6+5\\g(x)=2x-1[/tex]
Hence, two functions are [tex]f(x)=-2x+6,\; x<3\;\&\;g(x)=2x-1,\; x>3.[/tex]
Learn more about Inequality here:
https://brainly.com/question/3495453?referrer=searchResults
