Find the inverse of
y=6x2+4
Inverse of y=6x^2+4:
x=6y^2+4
6y^2=x-4
y^2=x/6 + 4/6
y^2=x/6 +2/3
y=sqroot(x/6 +2/3)
x=6y^2+4
6y^2=x+4
y^2=x/6 + 4/6
y^2=x/6 +2/3
y=sqroot(x/6 +2/3)
The three steps to inverse:
1. exchange x and y
2. solve for y in terms of x
3. check that f-1(f(x))=x
1.
y=6x²+4 => x=6y²+4
2.
x=6y²+4
6y²=x-4
y²=(x-4)/6
y=√((x-4)/6)
3.
√((6x²+4)-4)/6
=√(6x²/6)
=x
To find the inverse of the given equation, you need to interchange the x and y variables and solve for y.
Step 1: Start with the original equation:
y = 6x^2 + 4
Step 2: Swap the x and y variables:
x = 6y^2 + 4
Step 3: Solve for y. Rearrange the equation to isolate y by getting rid of the constant term and then dividing both sides by 6:
6y^2 = x - 4
y^2 = (x - 4) / 6
Step 4: Take the square root of both sides to solve for y:
y = ±√((x - 4) / 6)
Therefore, the inverse of the equation y = 6x^2 + 4 is:
y = ±√((x - 4) / 6)