Question

What is the range of the function f(x) = x4 – 2x2 + 1?

Answer 1

all real numbers greater than or equal to zero

Explanation:

The range of a function is defined as all possible output values it can take.

Now in our case, we have the function

`f(x)=x^4_{}-2x^2+1`

Since,

`x^4\ge2x^2`

for all values of x, this tells us that the expression

`x^4-2x^2+1`

will always be greater than zero.

Therefore, we can say

`f(x)=x^4_{}-2x^2+1\ge0`

This tells us that the range of the function is all real numbers greater than or equal to zero.

Therefore, the correct answer choice is the following.

all real numbers greater than or equal to zero