Question

For the function f defined by f(x)=3x^2−2x+5 find f(−x),−f(x) , and −f(−x).

Answer 1

Explanation:

Answer 2

`f(-x) = 3x^2+2x+5\\\\-f(-x) = -3x^2-2x-5\\\\-f(x) = -3x^2+2x-5`

Solution:

Given that the function is defined by,

`f(x) = 3x^2-2x+5`

We have to find f(-x) , -f(x) and -f(-x)

Let us first find f(-x)

Substitute x = -x in given function

`f(-x) = 3(-x)^2-2(-x)+5\\\\f(-x) = 3x^2+2x+5`

Now find -f(-x)

Multiply the above found f(-x) by negative sign

When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive.

`-f(-x) = -(3x^2+2x+5)\\\\-f(-x) = -3x^2-2x-5`

Now find -f(x)

Multiply the given function f(x) by negative sign

`-f(x) = -(3x^2-2x+5)\\\\-f(x) = -3x^2+2x-5`

Thus the values are found