00:01
We know find the domain of the composite function, f circle g of x, given that f of x equals 2x plus 1 over x minus 3, and g of x equals 5x minus 1.
00:13
So first we write down this composite function and this equals f of g of x.
00:21
So here, this is the input to the f function.
00:28
So first we have to determine if there are any domain restrictions to the input function.
00:33
The input function is g of x equals 5x minus 1.
00:38
Basically, this is a polynomial function, which is a linear function.
00:42
So this is defined for all real numbers.
00:45
It is defined from negative infinity to positive infinity.
00:50
So which means there are no domain restrictions on the input function g of x.
00:55
However, we will also have to check if there are any domain restrictions after calculating this f of g of x.
01:03
So first we calculate this f of g of x.
01:06
Now i replace this g of x as 5x minus 1...