Question

Hich of the following is an even function? f(x) = (x – 1)2 f(x) = 8x f(x) = x2 – x f(x) = 7

Answer 1

f(x) = 7 is an even function.

Explanation:

Any function is even when
`f(x) = f(-x)` and gives a graph that is symmetric with respect to the y-axis.

We are given these options and we have to check whether which of them is an even function:

`f(x)= (x-1)^2`
`= x^2-2x+1`

and
`f(-x) = (-x - 1)^2 = x^2 + 2x + 1` - This function is not even

`f(x) = 8x`

and
`f(-x) = -8x` - This function is not even

`f(x)=x^2-x`

and
`f(-x) = (-x)^2 + x = x² + x` - This function is not even

`f(x) = 7`

and
`f(-x) = 7` - EVEN FUNCTION

We get the same value for
`f(x)` and
`f(-x)`, therefore f(x) = 7 is an even function.