Advertisements
Advertisements
Question
Determine whether the following function is odd or even?
f(x) = `log (x^2 + sqrt(x^2 + 1))`
Advertisements
Solution
f(-x) = log((-x)2 + `sqrt((- x)^2 + 1)`
= log `(x^2 + sqrt(x^2 + 1))`
Thus f(-x) = f(x)
∴ f(x) is an even function.
APPEARS IN
RELATED QUESTIONS
Determine whether the following function is odd or even?
f(x) = x + x2
If f(x) = `x^3 - 1/x^3`, then show that `"f"(x) + "f"(1/x)` = 0
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)
If f(x) = ex and g(x) = loge x then find (fg)(1).
Draw the graph of the following function:
f(x) = |x – 2|
The graph of the line y = 3 is
Which one of the following functions has the property f(x) = `"f"(1/x)`?
The graph of f(x) = ex is identical to that of:
