how do you solve these problems?? (i already know the answers, i just don't understand how to solve it)
The function f is given by f(x)= x^2 - 6x + 13, for x is greater than and equal to 3.
1. write f(x) in the form (x-a)^2 + b
2. find the inverse function f^-1
for number two, wouldn't you just have to make it so x= y^2 - 6y + 13? or is it a different equation, because the right answer is squareroot of (x-4) - 3
The function f is given by f(x)= x^2 - 6x + 13, for x is greater than and equal to 3.
1. write f(x) in the form (x-a)^2 + b
2. find the inverse function f^-1
for number two, wouldn't you just have to make it so x= y^2 - 6y + 13? or is it a different equation, because the right answer is squareroot of (x-4) - 3
-
1 involves "completing the square" -- google it, you should find tutorial pages about it. i've given detailed answers on here before, so you could also search yahoo answers.
i can do it in my head but I'll give you a little hint:
[(x-3)^2 -9] +13 = (x-3)^2 + 4
to find the inverse function, it's easiest to work with our answer from #1
start with y=(x-3)^2 + 4 and solve for x (subtract 4 from both sides, take square root of both sides, then add 3 to both sides)
an inverse function simply undoes what another function does.
if f(x) adds 1 to x, written as f(x)=x+1, then the inverse function would subtract 1 from the argument.
so if you applied some function to x and then applied the inverse function to the result of the first function, you'd get back your original value of x. example:
f(x) = x+1
f^-1(z) = z-1
I use a different variable in the 2nd function so you don't get confused, but it doesn't matter, it's just a "placeholder". now follow this sequence. start with x. apply f(x) to it. we now have x+1. apply the inverse function to that. so we evaluate the function with z=x+1, which gives us (x+1)-1. and to nobody's surprise that equals just x, what we started with. you should do the same thing but with your problem so you really understand it.
i can do it in my head but I'll give you a little hint:
[(x-3)^2 -9] +13 = (x-3)^2 + 4
to find the inverse function, it's easiest to work with our answer from #1
start with y=(x-3)^2 + 4 and solve for x (subtract 4 from both sides, take square root of both sides, then add 3 to both sides)
an inverse function simply undoes what another function does.
if f(x) adds 1 to x, written as f(x)=x+1, then the inverse function would subtract 1 from the argument.
so if you applied some function to x and then applied the inverse function to the result of the first function, you'd get back your original value of x. example:
f(x) = x+1
f^-1(z) = z-1
I use a different variable in the 2nd function so you don't get confused, but it doesn't matter, it's just a "placeholder". now follow this sequence. start with x. apply f(x) to it. we now have x+1. apply the inverse function to that. so we evaluate the function with z=x+1, which gives us (x+1)-1. and to nobody's surprise that equals just x, what we started with. you should do the same thing but with your problem so you really understand it.