An inverse function is the function that reverses the original function.
The inverse function of [tex]\mathbf{y = 2x^2 + 2}[/tex] is: [tex]\mathbf{x = \sqrt{\frac{y -2}{2}} }[/tex]
The function is given as:
[tex]\mathbf{y = 2x^2 + 2}[/tex]
To calculate the inverse function, means we want to solve for x
So, we have:
[tex]\mathbf{y = 2x^2 + 2}[/tex]
Subtract 2 from both sides
[tex]\mathbf{y -2= 2x^2 }[/tex]
Divide both sides by 2
[tex]\mathbf{\frac{y -2}{2}= x^2 }[/tex]
Take square roots of both sides
[tex]\mathbf{\sqrt{\frac{y -2}{2}}= x }[/tex]
Rewrite as:
[tex]\mathbf{x = \sqrt{\frac{y -2}{2}} }[/tex]
Hence, the inverse function is:
[tex]\mathbf{x = \sqrt{\frac{y -2}{2}} }[/tex]
Read more about inverse functions at:
https://brainly.com/question/10300045
