Question

If f(×)= (×+1)(×^2-9) evaluate f(×-1)

Answer 1

So you have this function,

`\large\rm f(x)=(x+1)(x^2-9)`

Maybe ignore the x in the function for now.
Just think of it as an empty square that you fill in with something,

`\large\rm f(\square)=(\square+1)(\square^2-9)`

And they're asking us to simplify the function when the square is filled with x-1,

`\large\rm f(x-1)=([x-1]+1)([x-1]^2-9)`

You'll need to expand the (x-1)^2 term to (x^2-2x+1),

`\large\rm f(x-1)=([x-1]+1)([x^2-2x+1]-9)`

`\large\rm f(x-1)=(x-1+1)(x^2-2x+1-9)`

And then simplify further,

`\large\rm f(x-1)=(x)(x^2-2x-8)`

And distribute the x,

`\large\rm f(x-1)=x^3-2x^2-8x`