Question

find inverse of g(x)=2x^2-1

Answer 1

g(x)=2x^2-1

y = 2x^2 - 1

step1: interchange the x and y variables
---> x = 2y^2 - 1

step2: solve this new equation for y
2y^2 = x + 1
y^2 = (x+1)/2
y = ± √( (x+1)/2 )

Answer 2

[AI-generated answer — Step-by-Step Bot]

To find the inverse of a function, we need to switch the roles of x and y and then solve for y.

1. Start with the function g(x) = 2x^2 - 1.

2. Replace g(x) with y: y = 2x^2 - 1.

3. Swap x and y: x = 2y^2 - 1.

4. Solve this equation for y.

x = 2y^2 - 1
x + 1 = 2y^2
(x + 1) / 2 = y^2
√[(x + 1) / 2] = y (taking the square root of both sides)

5. The inverse function is given by: g^(-1)(x) = √[(x + 1) / 2].

Therefore, the inverse of g(x) = 2x^2 - 1 is g^(-1)(x) = √[(x + 1) / 2].