Question

Given z (x)=15x-x^2+3

Answer 1

○
`z(x - 1) = -x^2 + 17x - 13`

Explanation:

We are told that:

`z(x)= 15x - x^2 + 3`,

and told to find an expression for
`z(x - 1)`.

In order to find
`z(x - 1)`, we have to replace
`x` in the definition of
`z(x)` with
`(x-1)`:

`z(x - 1) = 15(x -1) - (x - 1)^2 + 3`

Now we can simplify:

⇒
`z(x-1) = 15x - 15 - (x - 1)^2 + 3` [Distributing 15 into the first brakets]

⇒
`z(x-1) = 15x - 15 - (x^2 - 2x + 1) + 3`

⇒
`z(x-1) = 15x - 15 - x^2 + 2x - 1 + 3` [Distributing the minus sign]

⇒
`z(x - 1) = 17x - x^2 -13` [Combining like terms]

⇒
`z(x - 1) = -x^2 + 17x - 13`

Therefore, the first option is the correct one.