# 7 - Functions Questions Answers

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**

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**Joshi sir comment**

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**

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**Joshi sir comment**

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

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

**Asked By: BONEY HAVELIWALA**

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**Joshi sir comment**

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**

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**Joshi sir comment**

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**

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**Joshi sir comment**

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

so 0 < log_{3}log_{2}x < ∞

so 1 < log_{2}x < ∞

so 2 < x < ∞

best calculus books for iitjee.

**Asked By: KRISHN RAJ**

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**Joshi sir comment**

its I. E. Maron

Let f(x) be a real valued function not identically equal to zero such that f(x+y^{n})=f(x)+(f(y))^{n}; y is real, n is odd and n >1 and f'(0) ³ 0. Find out the value of f '(10) and f(5).

**Asked By: KAMAL**

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**Joshi sir comment**

take x = 0 and y = 0 and n = 3

we get f(0) = f(0) + f(0)^{n} or f(0) = 0

now take x = 0, y = 1 and n = 3

so f(1) = f(0) + f(1)^{3}

so get f(1) = 1, other values are not excetable because f(x) be a real valued function not identically equal to zero and f'(0) ³ 0

similarly get the other values

you will get f(5) = 5

so f(x) = x generally then find f ^{' }(x) , i think it will be 1