00:02
We have the given functions as fx is equal to 3x minus 2 and g x is equal to x squared plus 5.
00:13
Now we have to find f of g of x and g of x and also the domain of g of x and g of x and also the domain of g of x and g of x.
00:38
So let's get started.
00:41
First of all, we'll find function f of g of x.
00:47
It can be also written as f of gx, that is 3 times gx minus 2 is equal to 3 times x squared plus 5 minus 2, which is equal to 3x square plus 5 minus 2, which is equal to 3x square plus 13.
01:10
So, f -not, f of g of x is 3x2 plus 13.
01:20
Similarly, g of f of x can be written as g of fx, which can be written as fx whole square plus 5, that is 3x minus 2 whole square plus 5.
01:42
And finally it comes to be.
01:46
9 x squared minus 12x plus 9 g of f of x after expanding the above function.
02:00
Now when we draw the graph of fx, it is something like that.
02:09
This is 0 .0 origin.
02:14
And this is graph of fx as equal to 3x minus 2.
02:21
This point is 2 by 3 .0.
02:27
So as this is continuous graph having no discontinuity from minus infinity to plus infinity, so it takes every value of x as its input...
