Question
How do I determine if a certain value is within the range of a function or not if it gives me an equation?
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Answer to a math question How do I determine if a certain value is within the range of a function or not if it gives me an equation?
Murray
4.592 Answers
1. Write down the equation you need to solve.
f(x) = c
where \( f(x) \) is the function and \( c \) is the given value.
2. Solve the equation for \( x \).
x = f^{-1}(c)
3. Check if the solution \( x \) is within the domain of \( f(x) \).
x \in \text{Domain of } f(x)
If \( x \) satisfies the domain condition, then \( c \) is within the range. Otherwise, it is not.
Answer: The value is within the range if \( x \) such that \( f(x) = c \) is within the domain of \( f(x) \).
where \( f(x) \) is the function and \( c \) is the given value.
2. Solve the equation for \( x \).
3. Check if the solution \( x \) is within the domain of \( f(x) \).
If \( x \) satisfies the domain condition, then \( c \) is within the range. Otherwise, it is not.
Answer: The value is within the range if \( x \) such that \( f(x) = c \) is within the domain of \( f(x) \).
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