00:01
As we practice this function notation, we have k of x is defined as negative x squared minus 6x plus 7.
00:13
And when we're asked to evaluate certain values, basically what's happening is everywhere we have in x, we replace it with that number.
00:23
So if we're doing k of zero, all these xes are going to be zero.
00:29
And this is a nice one because zero times anything is zero.
00:33
Just zero minus zero plus seven is going to be seven.
00:37
So do the same thing on the next one.
00:39
And again, if it helps write out everything without the x's and then fill in the blanks where k of six.
00:48
So negative of six squared would be, so you do six squared first and then negate it.
00:56
6 times 6 is also 36.
01:00
And so that should be negative 72 plus 7 is negative 65, which is going to be very different as when you we do k of negative 6.
01:13
And the reason for that, i like to put negatives in parentheses because really what's happening is you square negative 36.
01:24
You square the negative 6, so that is positive 36, and then you negate it.
01:31
And so what happens on this problem is these 36 will actually cancel, and you get positive 7 again.
01:38
So as i go back to k and just starting over, but this time we're doing the square root of 6, what happens is the square root of 6 cancels out with this square.
01:57
And i don't know if your teacher wants you to leave it as just negative 6, that you can add the 7 to minus 6 root 6.
02:07
So i might give you both answers of 1 minus 6 root 6...