Question

let f(x) = x²-x ,then f(x-1) - f(x+1) =​

Answer 1

Step-by-step explanation:

Let's simplify step-by-step.

f(x−1)−f(x+1)

Distribute:

=(f)(x)+(f)(−1)+−fx+−f

=fx+−f+−fx+−f

Combine Like Terms:

=fx+−f+−fx+−f

=(fx+−fx)+(−f+−f)

=−2f

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Answer 2

The value of f(x-1) - f(x+1) is - 4x + 1  

Given:

f(x) = x²- x      

To find:

Find the value of f(x-1) - f(x+1)  

Solution:

To find the value f(x-1) - f(x+1) calculate f(x-1) and f(x+1) as follows

To find f(x - 1) take x = (x - 1) in f(x)

f(x - 1) = (x - 1)² - (x - 1)  

= x² + 1² - 2x - x + 1

= x² - 3x + 2  

To find f(x+1) take x = (x + 1) in f(x)

f(x + 1) = (x + 1)² - (x + 1)

= x² + 1² + 2x - x - 1

= x² + x

Hence, f(x-1) - f(x+1) can be calculated as

f(x-1) - f(x+1) =  x² - 3x + 2 - (x² + x)

= x² - 3x + 1 - x² - x  

= - 4x + 1    

Therefore,

The value of f(x-1) - f(x+1) is - 4x + 1  

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