[tex]f(-x) = 3x^2+2x+5\\\\-f(-x) = -3x^2-2x-5\\\\-f(x) = -3x^2+2x-5[/tex]
Solution:
Given that the function is defined by,
[tex]f(x) = 3x^2-2x+5[/tex]
We have to find f(-x) , -f(x) and -f(-x)
Let us first find f(-x)
Substitute x = -x in given function
[tex]f(-x) = 3(-x)^2-2(-x)+5\\\\f(-x) = 3x^2+2x+5[/tex]
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.
[tex]-f(-x) = -(3x^2+2x+5)\\\\-f(-x) = -3x^2-2x-5[/tex]
Now find -f(x)
Multiply the given function f(x) by negative sign
[tex]-f(x) = -(3x^2-2x+5)\\\\-f(x) = -3x^2+2x-5[/tex]
Thus the values are found
