If f is a linear function such that f(-1) = 5 and f(2) = -1,then f(x + 1) = ?

You should notice that the function is linear, hence,
substituting x+1 for x in equation of a linear function
yields:

`f(x+1) = m(x+1)+n =gt f(x+1) = mx + m +
n`

Substituting -1 for `x+1` , or `x = -2` , in equation
above yields:

`f(-2) = -2m + m + n =gt 5 = -m +
n`

Substituting 2 for `x+1` , or `x = 2-1=1` , in equation
above yields:

`f(1)=m+m+n = 2m+n =gt 2m+n =
-1`

Subtracting the equation `-m+n=5`  from `2m+n = -1` 
yields:

2m+n+m-n=-1-5 => 3m = -6 => m =
-2

Substituting -2 for m in equation -m+n=5 yields `2+n=5
=gt n=5-2 =gt n=3` Hence, you need to substitute -2 for m and 3 for n in equation
`f(x+1) = -2x - 2+ 3 =gt f(x+1) = -2x +
1`

Hence, evaluating the equation of linear
function yields `f(x+1) = -2x + 1.`