c) A function $$ y=f(x) $$ is defined as follows: $$ f(x)=\left\{\begin{array}{ll}-2 & x \leq-1 \ x+1, & -1

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**Step 1. Evaluate $$ f(-1) $$:**

Since $$ x=-1 $$ satisfies $$ x \leq -1 $$, we use the first branch of the function:

$$
f(-1) = -2
$$

**Step 2. Evaluate $$ f(2) $$:**

Since $$ x=2 $$ satisfies $$ x \geq 2 $$, we use the third branch of the function:

$$
f(2) = 2^2 + 1 = 4 + 1 = 5
$$

**Step 3. Compute $$ f(-1) + f(2) $$:**

$$
f(-1) + f(2) = -2 + 5 = 3
$$

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**Step 4. Write an expression for $$ f(a^2+2) $$:**

Notice that for any real number $$ a $$, we have $$ a^2 \geq 0 $$, so

$$
a^2 + 2 \geq 2.
$$

Thus, for $$ x = a^2+2 $$ (which is always at least 2), we use the third branch of the function:

$$
f(a^2+2) = (a^2+2)^2 + 1.
$$
**i) Evaluate $$ f(-1) + f(2) $$:** - $$ f(-1) = -2 $$ - $$ f(2) = 5 $$ - $$ f(-1) + f(2) = 3 $$ **ii) Expression for $$ f(a^2+2) $$:** $$ f(a^2+2) = (a^2 + 2)^2 + 1 $$

c) A function is defined as follows:

i) Evaluate
ii) Write an expression for

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c) A function is defined as follows: i) Evaluate ii) Write an expression for