Advertisements
Advertisements
प्रश्न
If f(x) = `x^3 - 1/x^3`, then show that `"f"(x) + "f"(1/x)` = 0
योग
Advertisements
उत्तर
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.
shaalaa.com
Functions and Their Graphs
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
Determine whether the following function is odd or even?
f(x) = x2 – |x|
If f(x) = `((x + 1)/(x - 1))`, then prove that f(f(x)) = x.
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 (f + g)(1)
Draw the graph of y = 9 - x2.
The graph of y = 2x2 is passing through:
The minimum value of the function f(x) = |x| is:
f(x) = -5, for all x ∈ R is a:
The graph of f(x) = ex is identical to that of:
If f(x) = x2 and g(x) = 2x + 1 then (fg)(0) is:
