State true or false:
If $f (x) =$ $3 x^{4} - 5 x^{2} + k$ is an even function, then value of $k$ is even (where $k$ is a constant ).

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B False
If $f (x) =$ $3 x^{4} - 5 x^{2} + k$ is an even function
$f (- x) = 3 {(- x)}^{4} - 5 {(- x)}^{2} + k = 3 x^{4} - 5 x^{2} + k = f (x)$
which is even
$∴$ It is not depending on $k$ and it holds the same for any value of $k$ .
Therefore, $k$ can be any real number.

Suggest Corrections

Similar questions

Q. If

F (x) = 3 x^{4} - 5 x^{2} + k

, where

k

is a constant, is an even function, then find the value of

k

Q. Is the function

f (x) = K

, where

K

is constant, even or odd

Q. If

f (x) = 3 x^{4} - 5 x^{2} + k

is an even function, then which of the following describes the value of

k

(where

k

is a constant).

State if the given statement is True or False.

If h is even, j is odd, and k is odd, then is k ( h + j ) is odd.

If a function $y = f (x)$ is such that $f^{'} (x)$ is continuous function and satisfies $(f (x))^{2} = K + \int_{0}^{x} ((f (t))^{2} + (f^{'} (t))^{2}) d t, K ϵ R^{+}$ , then

Join BYJU'S Learning Program

State true or false:If f(x)=3x4−5x2+k is an even function, then value of k is even (where k is a constant ).

The correct option is B FalseIf f(x)= 3x4−5x2+k is an even functionf(−x)=3(−x)4−5(−x)2+k=3x4−5x2+k=f(x) which is even∴ It is not depending on k and it holds the same for any value of k. Therefore, k can be any real number.

State true or false:
If $f (x) =$ $3 x^{4} - 5 x^{2} + k$ is an even function, then value of $k$ is even (where $k$ is a constant ).

The correct option is B False
If $f (x) =$ $3 x^{4} - 5 x^{2} + k$ is an even function
$f (- x) = 3 {(- x)}^{4} - 5 {(- x)}^{2} + k = 3 x^{4} - 5 x^{2} + k = f (x)$
which is even
$∴$ It is not depending on $k$ and it holds the same for any value of $k$ .
Therefore, $k$ can be any real number.