00:02
Hi, we're given the function here, fx is equal to 4x squared minus x minus 3.
00:14
By the part here we have, this is the point minus 2 .15.
00:19
Is the point minus 2 .15 on the graph? so minus 2 .15 is it satisfying the given function or not? so just see that here.
00:29
You want to put here, take the function as and find out f of minus 2.
00:33
That is given as 4 times minus 2 square, minus minus 2.
00:39
Minus 3.
00:40
So that is given as 16 plus 2 minus 3.
00:47
That is coming out to 15.
00:48
So you can see that when you put here x is minus 2, we're getting as 15, the same point here.
00:53
Therefore, yes, it satisfies.
00:57
Yes, it is on the graph.
01:01
Yes, it is on the graph.
01:04
Okay.
01:06
If you move on to now, the b part, if x equals 2, what is happening? what point is on the graph of f if x equals two so we had equals two we're to find out f of two here there will be four times two square four times two square minus two minus three so that is given as 16 minus five that is 11 so it's going to be 11 here right a f x what point is on the graph of f x the point is given as 2 .11 the point is given as 2 .11 that is given as 2 .11 that is the point.
01:47
For the c part, if a fx is minus 3, so we have here 4x square minus x minus 3, this is equal to minus 3, right? it's equal to minus 3.
02:00
What is x? to solve for x here, so this cancels out, so we have 4x square minus x is equal to 0.
02:10
We factor out x here, we get 4x minus 1 is equal to 0.
02:17
This we have.
02:17
Right so we put each factor to 0 we get here x is equal to 0 or we have 4x minus 1 is equal to 0 so we get x is equal to 0 and then we have x is equal to 1 over 4 right x equal to 0 we have and then x is coming out to be 1 over 4 so the points are coming out to be here we have f x minus 3 right the point are coming out to be here 0.
02:46
Minus 3 that's 1 point and second is given as 1 over 4 minus 3.
02:52
That is the second point.
02:56
Next we have what about domain of f? so d part, it is 4x square minus x minus 3.
03:08
Well, it will be a parabola.
03:10
Opening upwards, right? so i just take an example here to find domain.
03:15
I just take an example here.
03:17
This is next.
03:18
This is y...