Sure, let's solve for [tex]\( f(4) \)[/tex] given the function [tex]\( f(x) = -2 \sqrt{9x} \)[/tex].
1. Identify the function and the input value:
We're given the function [tex]\( f(x) = -2 \sqrt{9x} \)[/tex] and we're asked to find the value of the function when [tex]\( x = 4 \)[/tex].
2. Substitute the given value into the function:
Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
f(4) = -2 \sqrt{9 \cdot 4}
\][/tex]
3. Perform the multiplication inside the square root:
Calculate the expression inside the square root:
[tex]\[
9 \cdot 4 = 36
\][/tex]
So, the expression simplifies to:
[tex]\[
f(4) = -2 \sqrt{36}
\][/tex]
4. Calculate the square root:
Find the square root of 36:
[tex]\[
\sqrt{36} = 6
\][/tex]
So, the expression now becomes:
[tex]\[
f(4) = -2 \cdot 6
\][/tex]
5. Multiply the remaining terms:
Finally, perform the multiplication:
[tex]\[
-2 \cdot 6 = -12
\][/tex]
Thus, the value of [tex]\( f(4) \)[/tex] is
[tex]\[
f(4) = -12.
\][/tex]
