what is the inverse of the function: y = x ^ 2 + 2?

Answer 1

This function does not have an inverse because it is not a 1-to-1 function. Only 1-to-1 functions have an inverse.

A function, f(x) is a 1-to-1 function if for every unique value of x produces a unique value for f(x). In other words, if two different values for x result in the same value for f(x), the function is not a 1-to-1 function. In the case of your function, f(x) = f(-x) (e.g., f(1) = f(-1) = 3; f(2) = f(-2) = 5, etc.), so it is obviously not a 1-to-1 function.

Answer 2

If we let f(x) = x² + 2 and the inverse of the function be g, then you have to find g such that f(g) = x. In other words:

x = g² + 2
g = ±(x - 2)^½

You can see that g is not a function because it is a parabola opening horizontally so it fails the vertical line test. The inverse of the function, g, is a relation rather than a function.

You can say that there is no inverse function because the inverse of f(x) is not a function.

Answer 3

y= x^2 +2
write x = y^2 + 2 (by replacing x with y and y with x)
Therefore y^2 = x - 2
or y = plus or minus square root of (x-2). It the inverse of the given function

Answer 4

y= 1/(x^2+2)

Answer 5

You'll have to approach this problem as follows:
y-2 = x ^ 2 (Subtract 2 from both sides)
+-sqrt(y-2)=x (Find square root of both sides)
y=+-sqrt(x-2) (Replace x by y and y by x)

Note sqrt is the square root and +- is plus or minus.

Answer 6

technically, there is no inverse to this function, because it's not one-to-one

Answer 7

y = x^2 + 2
x = y^2 + 2
x - 2 = y^2
y = sqrt(x - 2)

y^-1 = sqrt(x - 2)

Answer 8

y = +- sqrt (x-2)
that's y = plus minus sqrt (x-2)