Sure! Let's determine what [tex]\( f(x-3) \)[/tex] is given the function [tex]\( f(x) = 5x(x + 3) \)[/tex].
1. Start with the given function:
[tex]\[
f(x) = 5x(x + 3)
\][/tex]
2. Substitute [tex]\( x - 3 \)[/tex] in place of [tex]\( x \)[/tex] in the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(x - 3) = 5(x - 3) \left((x - 3) + 3\right)
\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[
(x - 3) + 3 = x
\][/tex]
4. Substitute back into the function:
[tex]\[
f(x - 3) = 5(x - 3)(x)
\][/tex]
5. Rearrange to make it look cleaner:
[tex]\[
f(x - 3) = 5x(x - 3)
\][/tex]
So, the expression for [tex]\( f(x-3) \)[/tex] is:
[tex]\[
f(x - 3) = 5x(x - 3)
\][/tex]
Hence, [tex]\( f(x-3) = 5x(x - 3) \)[/tex].
