Evaluating Composites of Functions
Answer:
[tex](f \circ g)(x)= -30[/tex]
Step-by-step explanation:
Please refer to my Answer from this Questions to know more about Composite Functions:
- brainly.com/question/24619506
- brainly.com/question/24614010
Given:
[tex]f(x) = -3x[/tex]
[tex]g(x) = |x -6|[/tex]
Please note that [tex](f \circ g)(x) = f(g(x))[/tex]. So, [tex](f \circ g)(-4) = f(g(-4))[/tex].
Before we can solve [tex]f(g(-4))[/tex], let's solve for [tex]g(-4)[/tex] first and you'll see why.
[tex]g(-4) = |-4 -6| \\ g(-4) = |-10| \\ g(-4) = 10[/tex]
Since [tex]\blue{g(-4)} = \blue{10}[/tex], [tex]f(\blue{g(-4)}) = f(\blue{10})[/tex].
Solving for [tex]f(10)[/tex]:
[tex]f(\blue{10}) = -3(\blue{10}) \\ f(\blue{10}) = -30[/tex]
