When f(x) = 9-3x and g(x) = 5x-7, find f(x)+g(x).
Understand the Problem
The question is asking us to find the sum of two functions, f(x) and g(x), given their definitions. We will substitute the values of f(x) and g(x) into the equation and simplify to get the result.
Answer
$$ f(x) + g(x) = 2 + 2x $$
Answer for screen readers
$$ f(x) + g(x) = 2 + 2x $$
Steps to Solve
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Define the Functions We have the functions given as:
$$ f(x) = 9 - 3x $$
$$ g(x) = 5x - 7 $$ -
Add the Functions Together We want to find ( f(x) + g(x) ). We can substitute the functions into the equation:
$$ f(x) + g(x) = (9 - 3x) + (5x - 7) $$ -
Combine Like Terms Simplify the expression by combining like terms:
$$ f(x) + g(x) = 9 - 3x + 5x - 7 $$
This simplifies to:
$$ = (9 - 7) + (-3x + 5x) $$
$$ = 2 + 2x $$ -
Final Result The final simplified form is:
$$ f(x) + g(x) = 2 + 2x $$
$$ f(x) + g(x) = 2 + 2x $$
More Information
The functions ( f(x) ) and ( g(x) ) are linear functions, and adding them together results in another linear function. The coefficient of ( x ) in the result indicates how steep the line will be, while the constant term shows where the line intersects the y-axis.
Tips
- Neglecting to combine like terms correctly.
- Forgetting to distribute negative signs when combining functions.
- Misunderstanding the operator when adding the functions (e.g., adding versus subtracting).
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