I can't wrap my mind around this statement...
The domain of f of g consists of the numbers x in the domain of g for which g(x) lies in the domain of f.
Question:
write formulas for f of g and g of f and find the domain and range.
f(x)= the square root of the quantity of x+1
g(x)= 1/x
f of g = square root of the quantity of 1/x +1
= square root of the quantity of (x+1)/x
so the domain can't equal 0 or the formula (x+1)/x >or=0 (but in this case can't be zero.)
but I don't remember now. I think we I am supposed to make a number line with the breaks 0 and the solution of (x+1)/x = 0 (which is -1)
so trying -2 gets +1/2 so that works then try...
-1/2 gets a negative number so it is out
then try 1 gets 2 so it works too.
(-infinity,-2] union (0, infinty)
but I don't think that is right and I don't know how to get the range
The domain of f of g consists of the numbers x in the domain of g for which g(x) lies in the domain of f.
Question:
write formulas for f of g and g of f and find the domain and range.
f(x)= the square root of the quantity of x+1
g(x)= 1/x
f of g = square root of the quantity of 1/x +1
= square root of the quantity of (x+1)/x
so the domain can't equal 0 or the formula (x+1)/x >or=0 (but in this case can't be zero.)
but I don't remember now. I think we I am supposed to make a number line with the breaks 0 and the solution of (x+1)/x = 0 (which is -1)
so trying -2 gets +1/2 so that works then try...
-1/2 gets a negative number so it is out
then try 1 gets 2 so it works too.
(-infinity,-2] union (0, infinty)
but I don't think that is right and I don't know how to get the range