Question

If f(x) = x*2-1, solve f (x+2)-
f(x-2) -16​

Answer 1

Step-by-step explanation:

Given :-

f(x) = x^2-1

To find:-

Solve f(x+2) -f(x-2)-16

Answer:-

Given that

f(x) = x^2-1

=> f(x+2) =(x+2)^2-1

We know that

(a+b)^2 = a^2+2ab+b^2

=> x^2+2(x)(2)+2^2-1

=> x^2+4x+4-1

=>x^2+4x+3

f(x+2)=x^2+4x+3

and

f(x-2) = (x-2)^2-1

We know that

(a-b)^2=a^2-2ab+b^2

=>x^2-2(x)(2)+2^2-1

=>x^2-4x+4-1

=>x^2-4x+3

f(x-2) = x^2-4x+3

Now

f(x+2) -f(x-2)-16

=> (x^2+4x+3 )-(x^2-4x+3)-16

=> x^2+4x+3-x^2+4x-3-16

=> (x^2-x^2)+(4x+4x)+(3-3-16)

=>0+8x+(-16)

=> 8x-16

Answer:-

The value of f(x+2) -f(x-2)-16 for the given problem is 8x-16

Used formulae:-

• (a+b)^2 = a^2+2ab+b^2

• (a-b)^2=a^2-2ab+b^2