CAT 1991 — QA Question 24
Use the following information:
Prakash has to decide whether or not to test a batch of 1000 widgets before sending them to the buyer. In case he decides to test, he has two options: (a) Use test I ; (b) Use test II. Test I cost Rs. 2 per widget. However, the test is not perfect. It sends 20% of the bad ones to the buyer as good. Test II costs Rs. 3 per widget. It brings out all the bad ones. A defective widget identified before sending can be corrected at a cost of Rs. 25 per widget. All defective widgets are identified at the buyer’s end and penalty of Rs. 50 per defective widget has to be paid by Prakash.
If y = f(x) and f(x) = , which of the following is true?
Answer & solution
- A
f(2x) = f(x) - 1
- B
x = f(2y) - 1
- C
f(1/x) = f(x)
x = f(y)
y = f(x) =
⇒ y(1 + x) = 1 – x
⇒ y + xy = 1 – x
⇒ x + xy = 1 – y
⇒ x(1 + y) = (1 – y)
⇒ x = = f(y)
Since here, y = f(x) and x = f(y), the given function refleccts on itself.
Hence, option (d).