The second question asks to determine the following for part (a):

Given functions $f(x) = x^2 - 3$ and $g(x) = x^2 + 3x + 5$, find $f(x) + g(x)$.

Solution:

We have: $f(x) = x^2 - 3$ $g(x) = x^2 + 3x + 5$

Now, add $f(x)$ and $g(x)$: $f(x) + g(x) = (x^2 - 3) + (x^2 + 3x + 5)$ $f(x) + g(x) = x^2 + x^2 + 3x - 3 + 5$ $f(x) + g(x) = 2x^2 + 3x + 2$

Final Answer:

$f(x) + g(x) = 2x^2 + 3x + 2$

Would you like further details or have any questions?

Here are 5 related questions to practice:

1. Calculate $f(x) - g(x)$ using the same functions.
2. Multiply $f(x) \times g(x)$ and simplify the result.
3. If $f(x) = x^2 - 3$ and $h(x) = 2x^3 - 4x + 1$, find $f(x) + h(x)$.
4. Solve for $x$ when $f(x) + g(x) = 0$.
5. Find the value of $f(x)$ and $g(x)$ at $x = 2$.

Tip: Always simplify your functions step by step to avoid mistakes.