# 7 - Functions Questions Answers

Maths >> Calculus >> Functions IIT JEE

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
is this question helpfull: 6 0 read solutions ( 1 ) | submit your answer
Joshi sir comment

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

Maths >> Calculus >> Functions IIT JEE

Let f(x) = x135 + x125 - x115 + x5 +1. If f(x) is divided by x3-x then the remainder is some function of x say g(x). Find the value of g(10)

Asked By: VAIBHAV GUPTA
is this question helpfull: 7 6 submit your answer
Joshi sir comment

for getting reminder put x3= x so

x135 + x125 - x115 + x5 +1 will give

x45 + x41*x2 - x38*x +x*x2 +1

x15 + x13*x2*x2 - x12*x2*x +x*x2 +1

x17 + x3 +1

x5*x2 + x + 1

x+ x + 1

x2*x + x +1

x3 + x +1

x+x+1

2x+1

now put x = 10

Maths >> Calculus >> Functions AIEEE

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

Asked By: BONEY HAVELIWALA
is this question helpfull: 4 0 submit your answer
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)

Maths >> Calculus >> Functions Others

Sir/Madam,

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

Asked By: BONEY HAVELIWALA
is this question helpfull: 1 2 read solutions ( 2 ) | submit your answer
Joshi sir comment

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

for ex.   0*(1111111111111111111111111) = 0

Maths >> Calculus >> Functions IIT JEE

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

Asked By: SIDDHANT
is this question helpfull: 4 0 submit your answer
Joshi sir comment

f(x)= log4log3log2

so 0 < log3log2x <

so 1 < log2x < ∞

so 2 < x <

Maths >> Calculus >> Functions IIT JEE

best calculus books for iitjee.

Asked By: KRISHN RAJ
is this question helpfull: 1 0 submit your answer
Joshi sir comment

its I. E. Maron

Maths >> Calculus >> Functions IIT JEE

Let f(x) be a real valued function not identically equal to zero such that f(x+yn)=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
is this question helpfull: 14 0 submit your answer
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

Register