Find the inverses of the following functions.
y = 3(x - 1)^2, x >= 1
Work:
x = 3(y - 1)^2
x = 3(y - 1)(y - 1)
x = 3(y^2 - y - y + 1)
x = 3y^2 - 6y + 3
And now what do I do!? Please explain and show me how to solve this inverse function!
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Thank you
x = 3(y - 1)^2 would be the inverse but you forgot the second part, y>=1
To find the inverse of a function, you need to switch the roles of the independent variable (x) and the dependent variable (y) and solve for y. In this case, we have the original equation x = 3y^2 - 6y + 3 and want to solve for y.
Step 1: Switch the roles of x and y.
x = 3y^2 - 6y + 3 becomes y = 3x^2 - 6x + 3
Step 2: Replace y with f^-1(x) to indicate the inverse function.
f^-1(x) = 3x^2 - 6x + 3
So, the inverse function of y = 3(x - 1)^2, x >= 1, is f^-1(x) = 3x^2 - 6x + 3.
The inverse function undoes the original function, so if you were to plug in f^-1(x) into the equation, the result would give you back the original value of x.
Keep in mind that for this particular function, it is only defined for x values greater than or equal to 1. Hence, the range of the inverse function will be restricted as well.