For the following function find $$ f(x+h) $$ and $$ f(x)+f(h) $$. $$ f(x)=x^{2}-12 $$ $$ f(x+h)=\square $$ (Simplify your answer.) $$ f(x)+f(h)=\square $$ (Simplify your answer.)

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UpStudy AI · Accepted Answer

Let's compute each expression step by step for the function $$ f(x) = x^{2} - 12 $$.

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### 1. Finding $$ f(x + h) $$

To find $$ f(x + h) $$, substitute $$ x + h $$ into the function in place of $$ x $$:

$$
f(x + h) = (x + h)^{2} - 12
$$

Now, expand the squared term:

$$
(x + h)^{2} = x^{2} + 2xh + h^{2}
$$

So,

$$
f(x + h) = x^{2} + 2xh + h^{2} - 12
$$

**Simplified Answer:**

$$
f(x + h) = x^{2} + 2xh + h^{2} - 12
$$

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### 2. Finding $$ f(x) + f(h) $$

First, compute $$ f(x) $$ and $$ f(h) $$ separately:

$$
f(x) = x^{2} - 12
$$
$$
f(h) = h^{2} - 12
$$

Now, add these two expressions together:

$$
f(x) + f(h) = (x^{2} - 12) + (h^{2} - 12)
$$
$$
f(x) + f(h) = x^{2} + h^{2} - 24
$$

**Simplified Answer:**

$$
f(x) + f(h) = x^{2} + h^{2} - 24
$$

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**Summary:**

$$
f(x + h) = x^{2} + 2xh + h^{2} - 12
$$
$$
f(x) + f(h) = x^{2} + h^{2} - 24
$$
$$ f(x + h) = x^{2} + 2xh + h^{2} - 12 $$ $$ f(x) + f(h) = x^{2} + h^{2} - 24 $$

For the following function find \( f(x+h) \) and \( f(x)+f(h) \). \( f(x)=x^{2}-12 \) \( f(x+h)=\square \) (Simplify your answer.) \( f(x)+f(h)=\square \) (Simplify your answer.)

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