To complete the statement [tex]\( f(6) = \)[/tex], we need to evaluate the function [tex]\( f(x) \)[/tex] at [tex]\( x = 6 \)[/tex].
Given the function:
[tex]\[ f(x) = 2x^2 + 5\sqrt{x - 2} \][/tex]
we will substitute [tex]\( x = 6 \)[/tex] into this function.
First, we calculate the term [tex]\( 2x^2 \)[/tex]:
[tex]\[ 2(6)^2 = 2 \cdot 36 = 72 \][/tex]
Next, we calculate the term [tex]\( 5\sqrt{x - 2} \)[/tex]:
[tex]\[ 5\sqrt{6 - 2} = 5\sqrt{4} = 5 \cdot 2 = 10 \][/tex]
Now, we add these two results together:
[tex]\[ 72 + 10 = 82 \][/tex]
Therefore,
[tex]\[ f(6) = 82 \][/tex]
So, the complete statement is:
[tex]\[ f(6) = 82 \][/tex]
