How do you find the inverse of each function?

Question

I need some math help please!!
f(x) = 2x^2
f(x) = -3x^2 -4

Answer 1

For one thing, these functions won't have inverses because their "inverses" will no longer be a function. I'll show you:

f(x) = 2x^2

Make f(x) as y.

y = 2x^2

To find the inverse, swap the x and y terms, and then solve for y.

x = 2y^2 {This is a sideways parabola}

If we go further,

y^2 = x/2, so
y = +/- sqrt(x/2)

The "plus or minus" is an indicator that this is not a function. Therefore it doesn't have an inverse.

Similarly for f(x) = -3x^2 - 4

Answer 2

write the equations in this form:
y=2x^2
y=-3x^2-4
now just make the x the subject of the equations,
x=sqrt(y/2)
x=sqrt((y+4)/-3)
then just swap the x and y around:
y=sqrt(x/2)
y=sqrt((x+4)/-3)
and those are the inverse functions

Answer 3

They don´t have inverse function because there are two x which give you the same f(x). x and (-x) give you the same f(x)