The inverse function is y = [tex] \sqrt{\frac{x + 3}{7}} [/tex].
You can find the inverse of any function by switching the x and y value. After doing so, you can solve for the new y. The result will be your inverse function. The step-by-step process for this one is below.
y = 7x^2 - 3 ----> Switch x and y
x = 7y^2 - 3 ----> Add 3 to both sides.
x + 3 = 7y^2 -----> Divide both sides by 7
[tex] \frac{x + 3}{7} [/tex] = y^2 ----> Take the square root of both sides
[tex] \sqrt{\frac{x + 3}{7}} [/tex] = y ---> Now switch the order so it is in a proper format.
y = [tex] \sqrt{\frac{x + 3}{7}} [/tex]
