reto wrote:
Which of the following functions f(x) satisfies the condition f(y-z) = f(y)-f(z) for all possible values of y and z?
A. f(x) = x2
B. f(x) = x + (x-1)2
C. f(x) = x-1
D. f(x) = 5/x
E. f(x) = x/5
Please anyone explain how this works efficiently. I always struggle when I see these function questions. What do do first? Plug in what into what? At first I did not understand what the question wanted with f(x) with regards to f(y-z)= .... for me, this feels like reading chinese
Note the phrasing of the question: "for all possible values of y and z". Only the right function will satisfy the condition for every possible value you choose; the other four answer choices may satisfy the condition for some values, but not for others.
Don't mess with the algebra, plug in easy numbers (for instance, z=1 and y=2) into each of the functions and POE. Keep plugging in and eliminate answer choices that do not meet the condition, until you are left with a single answer choice.
Plug in z = 1 and y = 2:
--> f(y-z) = f(2-1) = f(1) = 1-1 = 0
--> f(y) - f(z) = f(2) - f(1) = (2-1) - (1-1) = 1
Thus f(y-z) ≠ f(y) - f(z) for z=1 and y=2 and the answer is eliminated.
Please format your question properly. I think option A is \(x^2\) and not x2.
Whenever you see function questions, more often than not, you will be able to solve the questions by plugging in. Also, you need to understand what do you mean by 'f(x)'. It means that there is a relationship in x that is satisfied by all values of x.
In the given question, you need to evaluate all the given f(x) such that f(y-z)=f(y)-f(z) for
all y ,z (the underline portion means that the correct option HAS to be true for
any set of values of y and z).
Now, look at the first option,
f(x) = \(x^2\) (I am assuming that you wanted to write \(x^2\))
Do not worry about the variable being x,y or z. You just need to realize that there is a functional connection between the variables.
Now, assume y=4 and z=3
f(4-3)=f(1)=1^2=1
and f(4)=16 (substitute x=4 in f(x) = \(x^2\)), f(3)=9 and f(4)-f(3) = 7 not equal to f(4-3). Thus this version of f(x) is incorrect. Repeat the same (with the same set of numbers) and you will see that only E remains.
More questions to practice:
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