Answer :
To evaluate the function [tex]\( f(x) \)[/tex] when [tex]\( x = 6 \)[/tex], we need to consider the piecewise definition of the function:
1. If [tex]\(-4 < x < 6\)[/tex], then [tex]\( f(x) = 3x^2 + 1 \)[/tex].
2. If [tex]\( 6 \leq x < 9\)[/tex], then [tex]\( f(x) = 6 \)[/tex].
Since [tex]\( x = 6 \)[/tex] falls in the range [tex]\( 6 \leq x < 9\)[/tex], we use the second piece of the function, which is defined as [tex]\( f(x) = 6 \)[/tex].
Therefore, when [tex]\( x = 6 \)[/tex], the value of the function [tex]\( f(x) \)[/tex] is [tex]\( \boxed{6} \)[/tex].
1. If [tex]\(-4 < x < 6\)[/tex], then [tex]\( f(x) = 3x^2 + 1 \)[/tex].
2. If [tex]\( 6 \leq x < 9\)[/tex], then [tex]\( f(x) = 6 \)[/tex].
Since [tex]\( x = 6 \)[/tex] falls in the range [tex]\( 6 \leq x < 9\)[/tex], we use the second piece of the function, which is defined as [tex]\( f(x) = 6 \)[/tex].
Therefore, when [tex]\( x = 6 \)[/tex], the value of the function [tex]\( f(x) \)[/tex] is [tex]\( \boxed{6} \)[/tex].
