Answer:
○ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Step-by-step explanation:
We are told that:
[tex]z(x)= 15x - x^2 + 3[/tex],
and told to find an expression for [tex]z(x - 1)[/tex].
In order to find [tex]z(x - 1)[/tex], we have to replace [tex]x[/tex] in the definition of [tex]z(x)[/tex] with [tex](x-1)[/tex]:
[tex]z(x - 1) = 15(x -1) - (x - 1)^2 + 3[/tex]
Now we can simplify:
⇒ [tex]z(x-1) = 15x - 15 - (x - 1)^2 + 3[/tex] [Distributing 15 into the first brakets]
⇒ [tex]z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3[/tex]
⇒ [tex]z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3[/tex] [Distributing the minus sign]
⇒ [tex]z(x - 1) = 17x - x^2 -13[/tex] [Combining like terms]
⇒ [tex]z(x - 1) = -x^2 + 17x - 13[/tex]
Therefore, the first option is the correct one.
