find the value(s) of x for which f(x)=g(x).
f(x)=x^4-2x^2,g(x)=2x^2
set them equal, and solve for x
x^4-2x^2=2x^2
x^4-4x^2=0
(x^2-2x)(x^2+2x)=0
x^2(x-2)(x+2)=0
and now you have four solutions (two zeroes).
To find the value(s) of x for which f(x) is equal to g(x), we need to set the two functions equal to each other and solve for x.
Setting f(x) equal to g(x), we get:
x^4 - 2x^2 = 2x^2
To further simplify the equation, let's move all the terms to one side:
x^4 - 4x^2 = 0
Now, we can factor the equation:
x^2(x^2 - 4) = 0
The equation is now in factored form. To find the values of x, we set each factor equal to zero:
x^2 = 0 or x^2 - 4 = 0
Solving the first equation, we find x = 0.
For the second equation, let's solve it separately:
x^2 - 4 = 0
Adding 4 to both sides:
x^2 = 4
Taking the square root of both sides, we find:
x = ±2
Therefore, the values of x for which f(x) = g(x) are x = 0, x = 2, and x = -2.