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Let f:N→Z be defined by f(n)=n−1​/2 if n is odd and n/2​ when n is even. Determine the value of f(8).

User Robyn
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Final answer:

To determine the value of f(8) for the function defined, we use the rule for even numbers and divide 8 by 2, resulting in a value of 4.

Step-by-step explanation:

The student's question pertains to the function f defined for natural numbers that outputs integers. The function is defined differently depending on whether the input n is odd or even. For even numbers, f(n) = n/2, and for odd numbers, f(n) = (n-1)/2. To determine the value of f(8), we need to evaluate the function as per the instructions for even numbers.

To find f(8), establish whether 8 is even or odd. Since 8 is even, use the corresponding function rule. Calculate f(8) by dividing 8 by 2.

f(8) = 8/2
f(8) = 4

Therefore, the value of f(8) is 4.

Function evaluation refers to the process of determining the output value of a function for a given input or set of inputs. A function takes an input, performs some operations or computations on it, and produces an output according to a specific rule or formula.

User Arulmr
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