Functions Test ...

The minimum value of ax² + bx + c is 7/8 at x = 5/4. Find the value of the expression at x = 5, ifthe value of the expression at x = 1 is 1.

A function a(x) is defined for x as 3a(x) + 2a (2 – x) = (x + 3)². What is the value of [G (–5)]

where [x] represents the greatest integer less than or equal to x?

Find the domain of the definition of the functiony = [(x – 3)/(x + 3)]^1/2 + [(1 – x)/(1 + x)]1/2.

If f(x) = e^x and g(x) = log_ex then value of fog will be

The function y = 1/x shifted 1 unit down and 1 unit right is given by

If f(x) = |x – 2| , then which of the following is always true?

Read the instructions below and solve:
f(x) = f(x – 2) – f(x – 1), x is a natural number
f(1) = 0, f(2) = 1

Q.

The value of f[f(6)] is

If f(x) is a function satisfying f(x). f(1/x) = f(x) + f(1/x) and f(4) = 65, what will be the value off(6)?

Define the functions:
A(x, y, z) = Max (max (x, y), min (y, z) min (x, z))
B(x, y, z) = Max (max (x, y), min (y, z) max (x, z))
C(x, y, z) = Max (min (x, y), min (y, z) min (x, z))
D(x, y, z) = Min (max (x, y), max (y, z) max (x, z))
Max (x, y, z) = Maximum of x, y and z.
Min (x, y, z) = Minimum of x, y and z.
Assume that x, y and z are distinct integers.

Q.

For what condition will A(x, y, z) be equal to Max (x, y, z)?

Define the functions:
A(x, y, z) = Max (max (x, y), min (y, z) min (x, z))
B(x, y, z) = Max (max (x, y), min (y, z) max (x, z))
C(x, y, z) = Max (min (x, y), min (y, z) min (x, z))
D(x, y, z) = Min (max (x, y), max (y, z) max (x, z))
Max (x, y, z) = Maximum of x, y and z.
Min (x, y, z) = Minimum of x, y and z.
Assume that x, y and z are distinct integers.

Q.

For what condition will A(x, y, z) not be equal to B (x, y, z)?

Define the functions:
A(x, y, z) = Max (max (x, y), min (y, z) min (x, z))
B(x, y, z) = Max (max (x, y), min (y, z) max (x, z))
C(x, y, z) = Max (min (x, y), min (y, z) min (x, z))
D(x, y, z) = Min (max (x, y), max (y, z) max (x, z))
Max (x, y, z) = Maximum of x, y and z.
Min (x, y, z) = Minimum of x, y and z.
Assume that x, y and z are distinct integers.

Q.

The highest value amongst the following will be

A0, A1, A2,...... is a sequence of numbers withA0 = 1, A1 = 3, and At = (t +1) At–1 – t At–2 = 2, 3, 4,....Conclusion I. A8 = 77Conclusion II. A10 = 121Conclusion III. A12 = 145

The figure below shows the graph of a function f (x). How many solutions does the equation f ( f(x)) = 15 have?

For all real numbers x, except x = 0 and x = 1, the function F is defined by 

If 0 < a < 90° then F((cosec a)2) =

where [x] is defined as integral part of x and f is a fraction, then x(1 – f) equals–