I need help solving this problem f(x)=2x^2+1 find and simplify f(x+2)-f(x)/2?

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I need help solving this problem f(x)=2x^2+1 find and simplify f(x+2)-f(x)/2?

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Answer 1 · 2017-02-02T16:42:55

$f (x + 2) - \frac{f (x)}{2} = x^{2} + 8 x + \frac{17}{2}$ $f(x+2)-f(x)/2=x^2+8x+17/2$

Explanation:

$f (x) = 2 x^{2} + 1$ $f(x) = 2x^2 + 1$

$f (x + 2) - \frac{f (x)}{2}$ $f(x+2) - f(x)/2$

First, find $f (x + 2)$ $f(x+2)$ by plugging $x + 2$ $x+2$ into the original equation

$f (x + 2) = 2 {(x + 2)}^{2} + 1$ $f(x+2) = 2(x+2)^2 + 1$
$f (x + 2) = 2 (x^{2} + 4 x + 4) + 1$ $f(x+2) = 2(x^2+4x+4) + 1$
$f (x + 2) = 2 x^{2} + 8 x + 9$ $f(x+2) = 2x^2+8x+9$

Next, find $\frac{f (x)}{2}$ $f(x)/2$ by substituting $2 x^{2} + 1$ $2x^2+1$ for $f (x)$ $f(x)$

$\frac{f (x)}{2} = \frac{2 x^{2} + 1}{2}$ $f(x)/2 = (2x^2+1)/2$
$\frac{f (x)}{2} = x^{2} + \frac{1}{2}$ $f(x)/2 = x^2+1/2$

Combine your answers for the final answer by substitution

$f (x + 2) - \frac{f (x)}{2}$ $f(x+2) - f(x)/2$
$= (2 x^{2} + 8 x + 9) - (x^{2} + \frac{1}{2})$ $= (2x^2+8x+9) - (x^2+1/2)$
$= x^{2} + 8 x + \frac{17}{2}$ $=x^2+8x+17/2$

Answer 2 · 2017-02-02T16:45:27

$x^{2} + 8 x + \frac{17}{2}$ $x^2+8x+17/2$

Explanation:

$f (x + 2) - \frac{f (x)}{2}$ $f(x+2)-f(x)/2$
$" "$
$= 2 {(x + 2)}^{2} + 1 - \frac{2 x^{2} + 1}{2}$ $=2(x+2)^2+1-(2x^2+1)/2$
$" "$
$= 2 (x^{2} + 4 x + 4) + 1 - \frac{2 x^{2}}{2} - \frac{1}{2}$ $=2(x^2+4x+4)+1-(2x^2)/2-1/2$
$" "$
$= 2 x^{2} + 8 x + 8 + 1 - x^{2} - \frac{1}{2}$ $=2x^2+8x+8+1-x^2-1/2$
$" "$
$= 2 x^{2} - x^{2} + 8 x + 8 + 1 - \frac{1}{2}$ $=2x^2-x^2+8x+8+1-1/2$
$" "$
$= x^{2} + 8 x + \frac{17}{2}$ $=x^2+8x+17/2$

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I need help solving this problem f(x)=2x^2+1 find and simplify f(x+2)-f(x)/2?

2 Answers

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