Answer :

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].