Functions

Q. If $f\left(x\right)=x^2+2x-5$ and g(x) = 5x + 30, then the roots of the quadratic equation g[f(x)] will be

1. $1,2$
2. $-1,-1$
3. $-1+\sqrt{2},-1-\sqrt{2}$
4. $2,-1$

Q. $f_1=2,f_2=3$
$f_n=f_{n+1}-f_{n+2}$ for n $\ge$ 1, then what is $f_{123}$?

1. -2
2. -1
3. 1
4. 2

Q. What is the maximum and the minimum values of the function,
$f\left(x\right)=\frac{x^2+2x+1}{x^2+2x+7}$

1. 4, 2
2. 2, 1
3. None of these
4. 1, 0

Q. What is the range of $f\left(x\right)=\frac{1}{x^2+6x+6}$

1. $(-\infty ,\frac{1}{3}]\cup [0,\infty )$
2. $(-\infty ,\frac{1}{3}]\cup (0,\frac{1}{3}]$
3. $(0,\infty )$
4. $(-\infty -\frac{1}{3}]\cup (0,\infty )$

Q. For all non - negative integers x and y, f(x, y) is defined as below.
f(0, y) = y + 1
f(x + 1, 0) = f(x, 1)
f(x + 1, y + 1) = f(x, f(x + 1, y)) find f(1, 2)?

1. 2
2. 4
3. 3
4. Cannot be determined

Q. Find the value of 'x' for which it satisfies the inequality |x - 2| + |x - 3| + |x - 4| $\ge$ 9.

1. $x\le 0orx\ge 6$
2. $x\le -2orx\ge 3$
3. $-2\le x<3$
4. $0\le x\le 6$

Q. f(x) = $x^3$ + x + 5
g(x) = $x^2$ + 9 + $\frac{1}{x}$
find fog/gof for x = 1?

1. $\frac{1622}{104}$
2. $\frac{5115}{213}$
3. $\frac{9429}{407}$
4. $\frac{8203}{347}$

Q. Find the solution set for [3x] + [4x] + [5x] = 14, where [] indicates the greatest integer function.

1. $x<\frac{3}{2}$
2. $1\le x$ < $\frac{4}{3}$
3. x > $\frac{3}{2}$
4. $\frac{5}{4}\le$x < $\frac{27}{20}$

Q. Find the value of $\left[\frac{1}{8}\right]+[\frac{1}{8}+\frac{1}{400}]+[\frac{1}{8}+\frac{1}{200}]+[\frac{1}{8}+\frac{3}{400}]+\cdots +[\frac{1}{8}+\frac{399}{400}]$ if [x] denotes the integral part of x for real x.

1. 75
2. 50
3. 25
4. Cannot be determined

Q. The sum of two even functions is always:

1. Even function
2. Inverse Function
3. Odd function
4. Can be odd or even