Answer:
[tex]\boxed{f(6) = 34}[/tex]
Step-by-step explanation:
Composition of functions occurs when we have two functions normally written similar or exactly like f(x) & g(x) - you can have any coefficients to the (x), but the most commonly seen are f(x) and g(x). They are written as either f(g(x)) or (f o g)(x). Because our composition is written as [tex](f \circ g)(2)[/tex], we are replacing the x values in the g(x) function with 2 and simplifying the expression.
[tex]g(2) = 3(2)[/tex]
[tex]g(2) = 6[/tex]
Now, because we are composing the functions, this value we have solved for now replaces the x-values in the f(x) function. So, f(x) becomes f(6), and we use the same manner as above to simplify.
[tex]f(6) = (6)^2-2[/tex]
[tex]f(6) = 36-2[/tex]
[tex]f(6) = 34[/tex]
Therefore, when we compose the functions, our final answer is [tex]\bold{f(6) = 34}[/tex].
