If f(x) = x^2 + 3x + 2 and g(x) = -3x, find (f + g)(-2).
Understand the Problem
The question is asking to find the value of the sum of two functions, f and g, at a specific input, which is -2. We will first evaluate f(-2) and g(-2), and then sum these values to obtain (f + g)(-2).
Answer
$(f + g)(-2) = 6$
Answer for screen readers
$(f + g)(-2) = 6$
Steps to Solve
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Evaluate f(-2) To find $f(-2)$, substitute $x = -2$ into the function $f(x)$. $$ f(-2) = (-2)^2 + 3(-2) + 2 $$ Calculating this gives: $$ f(-2) = 4 - 6 + 2 = 0 $$
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Evaluate g(-2) Next, evaluate $g(-2)$ by substituting $x = -2$ into the function $g(x)$. $$ g(-2) = -3(-2) $$ Calculating this gives: $$ g(-2) = 6 $$
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Sum the values of f(-2) and g(-2) Now, add $f(-2)$ and $g(-2)$ to find $(f + g)(-2)$. $$ (f + g)(-2) = f(-2) + g(-2) = 0 + 6 $$ Calculating this gives: $$ (f + g)(-2) = 6 $$
$(f + g)(-2) = 6$
More Information
The functions were evaluated at a specific input, and the results were summed to find the combined output at that input. This method can be applied to any two functions to find their sum at a given value.
Tips
- Miscalculating the values of the functions at the specified input.
- Forgetting to add the results together after evaluating both functions.
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