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
g(x) = 3-5sin(2x-4)
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)
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
x7 + x + 1
x2*x + x +1
x3 + 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)= ?
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=∞.
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 ?
f(x)= log4log3log2x
so 0 < log3log2x < ∞
so 1 < log2x < ∞
so 2 < x < ∞
best calculus books for iitjee.
its I. E. Maron
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).
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