# 14 - Functions Questions Answers

x+y =[x] +[y] { where [.] denotes the greatest integer function of x},, then find lines on which the non integral solutions to this equation lie.??????????

**Asked By: SHALEEN**3 year ago

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**Asked By: YAWAR SHAH**3 year ago

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Find a formula for a function g(x) satisfying the following conditions

a) domain of g is (-∞ , ∞ ) b) range of g is [-2 , 8] c) g has a period π d) g(2) = 3

**Asked By: VAIBHAV GUPTA**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

g(x) = 3-5sin(2x-4)

Let f(x) = x^{135} + x^{125} - x^{115 }+ x^{5} +1. If f(x) is divided by x^{3}-x then the remainder is some function of x say g(x). Find the value of g(10)

**Asked By: VAIBHAV GUPTA**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

for getting reminder put x^{3}= x so

x^{135} + x^{125} - x^{115 }+ x^{5} +1 will give

x^{45} + x^{41}*x^{2} - x^{38}*x +x*x^{2} +1

x^{15} + x^{13}*x^{2}*x^{2} - x^{12}*x^{2}*x +x*x^{2} +1

x^{17 }+ x^{3} +1

x^{5}*x^{2} + x + 1

x^{7 }+ x + 1

x^{2}*x + x +1

x^{3} + x +1

x+x+1

2x+1

now put x = 10

Find out for what integral values of n the number 3π is a period of the function :

f(x) = cos nx . sin(5/n)x

**Asked By: VAIBHAV GUPTA**5 year ago

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Suppose that f is a function such that f(cos x) = cos 17x . Which one of the following functions g has the property that g(sin x) = sin 17x .

(A) g(x) = f(√1-x^{2}) (B) g(x) = f(x - π/4) (C) g(x) = √1-x^{2 }(D) g(x) = f(x)

**Asked By: VAIBHAV GUPTA**5 year ago

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if ƒ:R−{0} -> R, 2ƒ(x) − 3ƒ(1⁄x) = x² then ƒ(3)= ?

**Asked By: BONEY HAVELIWALA**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

2ƒ(x) − 3ƒ(1⁄x) = x² (1)

so 2ƒ(1/x) − 3ƒ(x) = 1/x² (2)

multiply (1) to 2 and (2) to 3, then add the two equations, you will get f(x) then calculate f(3)

Sir/Madam,

Suddenly a question struck on my mind: 0×∞= 1 or 0?? as 1⁄0=∞.

**Asked By: BONEY HAVELIWALA**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

it will be 0, assume it by considering that ∞ is a big number

for ex. 0*(1111111111111111111111111) = 0

FIND DOMAIN OF f(x)=log4log3 log2x WHERE 4,3,2 ARE BASES ?

**Asked By: SIDDHANT**5 year ago

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**Answer Strategies and trick by Manish sir**(it will help you to solve it by yourself)

f(x)= log_{4}log_{3}log_{2}x

so 0 < log_{3}log_{2}x < ∞

so 1 < log_{2}x < ∞

so 2 < x < ∞

## If f be decreasing continuous function satisfying f(x+y)=f(x)+f(y) for all x,y belongs to R; f'(0)=-1, then

##
** 1**

## ∫ f(x)dx is

##
**0**

**A. 1 **

**B. 1-e**

**C.2-e**

**D. none of these**

**Asked By: MOHIT SAINI**6 year ago

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