Question

If f(x)=x^2+5 find f(x+2)-f(x-2).

Answer 1

Answer:

$8x$

Step-by-step explanation:

put the value of $x+2$ in place of $x$ in first case and $x-2$ in second case and substract the the function value for the first from the value of the function in second case.

Step 1 of 3:

$f(x+2)= (x+2)^2+5$

Step 2 of 3:

$f(x-2)= (x-2)^2+5$

Step 3 of 3:

$f(x+2)-f(x-2) &=& (x+2)^2+5-[(x-2)^2+5]\\ &=& (x+2)^2+5-(x-2)^2-5\\\\ &=& (x+2)^2-(x-2)^2+5-5\\\\=(x+2)^2-(x-2)^2$

Using the formula,  , $a^2-b^2=(a-b)(a+b)$ , the eqution will become:

$(x+2+x-2)(x+2-x+2)\\=(2x)(4)\\=8x$

Hence, $f(x+2)-f(x-2)$ $= 8x$