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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Murray

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75 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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