We are given two functions:

$f(x) = -2x + 5$ $g(x) = x^2 - 1$

We need to calculate $f(-3) + g(2)$.

Step 1: Calculate $f(-3)$

Substitute $x = -3$ into the function $f(x)$:

$f(-3) = -2(-3) + 5$ $f(-3) = 6 + 5 = 11$

Step 2: Calculate $g(2)$

Substitute $x = 2$ into the function $g(x)$:

$g(2) = 2^2 - 1$ $g(2) = 4 - 1 = 3$

Step 3: Add the results

Now, add the results of $f(-3)$ and $g(2)$:

$f(-3) + g(2) = 11 + 3 = 14$

Final Answer:

$f(-3) + g(2) = 14$

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Would you like any more details or have any further questions?

Here are some related questions you might find interesting:

1. What is the domain and range of the function $f(x) = -2x + 5$?
2. How can you find the intersection points of the functions $f(x)$ and $g(x)$?
3. What would happen to the result of $f(-3) + g(2)$ if we change the coefficients of $f(x)$ and $g(x)$?
4. How would you calculate $f(x) + g(x)$ for any given $x$?
5. Can you find the inverse of $g(x) = x^2 - 1$?

Tip: Always carefully substitute the given values into the functions to avoid calculation errors!