Question

For the function g(x)= -2(x-1)^2 +7 How do I define the equation of g^-1 by switching the operations

Answer 1

g(x) = -2(x-1)^2 + 7

to find the inverse g^-1 we swap the x and the y such that y=g^-1(x)

x = -2(y -1)^2 + 7

solving for y:

x = -2(y -1)^2 + 7
-(x - 7)/2 = (y - 1)^2
y - 1 = +- sqrt((7 - x)/2)
y = 1 +- sqrt((7 - x)/2)

thus

g^-1(x) = 1 +- sqrt((7 - x)/2)

Answer 2

wait so you brought the -2 to the other side?

Answer 3

indeed i did

Answer 4

well i multiplied both sides by -2 to eliminate the denominator on the right

Answer 5

ah ok, thanks