determine the inverse of h(x)=sqrt of 12-4x
To find the inverse of the function h(x) = √(12-4x), we will first find the inverse function by swapping the variables x and y and then solving for y.
The original function is h(x) = √(12-4x)
Let y = √(12-4x)
Swap x and y:
x = √(12-4y)
Now solve for y:
Square both sides to get rid of the square root:
x^2 = 12 - 4y
Rearrange the equation to solve for y:
4y = 12 - x^2
y = (12 - x^2)/4
y = 3 - x^2/4
Therefore, the inverse function h^(-1)(x) = 3 - x^2/4