Question

Decide whether f is even, odd, or neither f(x)=x4-2x2 + 6 Choose the correct statement O A. The function is even O B. The function is odd. O C. The function is neither even nor odd

Answer 1

It is given that,

f(x) = x⁴ - 2x² + 6

Lets put any odd number in the given function that is either 1, 3, 5, 7, and so on.

Put x = 1

f(1) = (1)⁴ - 2(1)² + 6

f(1) = 1 - 2 + 6

f(1) = 5

Now put x = 3

f(3) = (3)⁴ - 2(3)² + 6

f(3) = 81 - 18 + 6

f(3) = 69

Hence it has been observed that if we put any odd number in place of 'x', the result is an odd number.

Now lets put any even number in the given function that is either 2, 4, 6, 8, and so on.

Put x = 2

f(2) = (2)⁴ - 2(2)² + 6

f(2) = 16 - 8 + 6

f(2) = 14

Now put x = 4

f(4) = (4)⁴ - 2(4)² + 6

f(4) = 256 - 32 + 6

f(4) = 230

Hence it has been observed that if we put any even number in place of 'x', the result is an even number.

Therefore it has been concluded that the function is neither even nor odd

So the answer is option (c), that is ' The function is neither even nor odd'.

Answer 2

OPTION A : The function is even.

[ f(-x) = (-x)^4 - 2(-x)^2 + 6 = x^4 - 2x^2 + 6 = f(x)

So, the function is even ]