Advertisements
Advertisements
Question
If f(x) = `x^3 - 1/x^3`, then show that `"f"(x) + "f"(1/x)` = 0
Advertisements
Solution
f(x) = `x^3 - 1/x^3` .....(1)
`"f"(1/x) = (1/x)^3 - 1/(1/x)^3`
`= 1/x^3 - x^3` ....(2)
(1) + (2) gives
`"f"(x) + "f"(1/x) = x^3 - 1/x^3 + 1/x^3 - x^3` = 0
Hence Proved.
APPEARS IN
RELATED QUESTIONS
Determine whether the following function is odd or even?
f(x) = `log (x^2 + sqrt(x^2 + 1))`
Determine whether the following function is odd or even?
f(x) = x + x2
For f(x) = `(x - 1)/(3x + 1)`, write the expressions of `"f"(1/x) and 1/("f"(x))`
If f(x) = ex and g(x) = loge x then find (3f) (1).
Draw the graph of the following function:
f(x) = |x – 2|
Draw the graph of the following function:
f(x) = e-2x
Draw the graph of y = 9 - x2.
The graph of the line y = 3 is
If f(x) = 2x and g(x) = `1/2^x` then (fg)(x) is:
If f(x) = x2 and g(x) = 2x + 1 then (fg)(0) is:
