An object with a height of 4.31 cm is placed 12.6 cm from a concave mirror. determine the radius of the mirror if the image appears 8.77 cm from the mirror. also determine the image height. 4. repeat question 6 but for a convex mirror.

Explanation:

Given that,

Height of object = 4.31 cm

Distance of the object = -12.6 cm

Distance of the image = -8.77 cm

For concave mirror,

Using mirror's formula

Radius of the mirror is

The magnification of the mirror,

Now, For convex mirror,

Using mirror's formula

Radius of the mirror is

The magnification of the mirror,

Hence, This is the required solution.

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .