Question

How do you evaluate `f(x+1)` given the function `f(x)=3-\frac{1}{2} x`?

Answer 1

See a solution process below:

Explanation:

To evaluate `f(x + 1)` substitute `color(red)((x + 1))` for each occurrence of `color(red)(x)` in `f(x)` and calculate the result:

`f(color(red)(x)) = 3 - 1/2color(red)(x)` becomes:

`f(color(red)(x + 1)) = 3 - 1/2color(red)((x + 1))`

`f(color(red)(x + 1)) = 3 - 1/2x - (1/2 * 1)`

`f(color(red)(x + 1)) = 3 - 1/2x - 1/2`

`f(color(red)(x + 1)) = 3 - 1/2 - 1/2x`

`f(color(red)(x + 1)) = (2/2 * 3) - 1/2 - 1/2x`

`f(color(red)(x + 1)) = 6/2 - 1/2 - 1/2x`

`f(color(red)(x + 1)) = (6 - 1)/2 - 1/2x`

`f(color(red)(x + 1)) = 5/2 - 1/2x`

Or

`f(color(red)(x + 1)) = (5 - x)/2`