f(x) = -log₂x
The given function is f(x) = -log₂x
The given function is f(x) = -log₂x. Let’s break it down step by step:
1. Logarithm: A logarithm is the inverse operation of exponentiation. It tells us what exponent we need to raise a base to in order to obtain a given number. In this case, we have a logarithm with base 2, denoted as log₂. So, log₂x represents the exponent to which we need to raise 2 to get x.
2. Negative Sign: The negative sign (-) in front of the logarithm indicates that the logarithm value will be negated or multiplied by -1. In other words, the negative sign flips the sign of the logarithm result.
3. Function Notation: The function is represented as f(x), which is a way of expressing the relationship between the input (x) and the output (f(x)). It signifies that the value of f is dependent on the value of x.
Putting it all together, the function f(x) = -log₂x means that we are taking the logarithm of x with base 2, and then multiplying the result by -1. Therefore, the function takes an input value x, finds the logarithm of x with base 2, and then flips the sign of the result.
A couple of additional points to note:
– The domain of the function is all positive real numbers because the logarithm of a negative number or zero is undefined.
– The range of the function is all real numbers because the logarithm of a positive number can be any real value.
I hope this explanation helps! If you have any further math-related questions, feel free to ask.
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