Question

If f(x) =  4x − x², x ∈ R, then write the value of f(a + 1) −f(a − 1).

 

Answer 1

Given:
f(x) =  4x − x², x ∈ R
Now,
f(a + 1) = 4(a + 1)  -(a + 1)²
             = 4a + 4 -(a² + 1 + 2a)
             = 4a + 4 -a² -1 - 2a 
             = 2a -a² + 3
f(a -1) = 4(a -1) - 1) +1)²
             = 4a-4 - (a² + 1 -2a)
             = 4a - 4 - a² -1 + 2a 
             = 6a - a² -5
Thus,
f(a + 1) − f(a − 1) = ( 2a -a² + 3) -(6a -a² -5)
                             = 2a -a² + 3 -6a + a² + 5
                             =  8 -4a
                             = 4(2 -a)