The graph of f(x) shown below has the same shape as the graph of g(x) = x^2, but it is shifted up 1 unit. what is the equation?

Step-by-step explanation:

we have

This is the equation of a vertical parabola open upward

The vertex is a minimum

The vertex is the point (0,0)

The graph of f(x) has the same shape as the graph of g(x), but is shifted up 1 unit

so

The vertex of the function f(x) is (0,1)

The rule of the translation of g(x) to f(x) is

(x,y) ----> (x,y+1)

therefore

The equation of f(x) is equal to

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.