Question

if f(x) =x^4 +4 find f(x+1 ) - f(x-1)​

Answer 1

Answer:

8x(x²+1)

Step-by-step explanation:

f(x)=x⁴ + 4

f(x+1)=(x+1)⁴ +4

f(x-1)=(x-1)⁴+4

f(x+1)-f(x-1)=(x+1)⁴+4 - (x-1)⁴-4

                =((x+1)²)²-((x-1)²)²

               =((x+1)²+(x-1)²)((x+1)²-(x-1)²)                [a²-b²=(a+b)(a-b)]

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

               = (2x²+2)(4x)

                =8x(x²+1)