Domain and Range Question? (Checking if I have correct answer)?

1) Domain is (1/2, inf) because 1/2 would give you ln(ln(1)) = ln(0) which is undefined, and greater values would give you a number higher than 1 in the inside ln. Your range is correct.

2) The domain is (0, 1/2). Your range is correct.

3) The domain is (0,1/2). If x>1/2 then your second term will have a negative number inside the ln. Your range is correct.

area: set of numbers we are able to apply as x selection: set of numbers we get out from function as quickly as we tried each attainable x if we don't evaluate complicated numbers93e7709cfdece731b854c055e03e8565 and cut back our prognosis to R93e7709cfdece731b854c055e03e8565 we start up up by making use of watching the function itself: x^0,2 could paintings for all numbers yet on account that that's under root93e7709cfdece731b854c055e03e8565 and root only works on effective numbers we get to our limit that (4-3^0,2 ought to no longer be unfavorable. that's 0 and that's effective yet no longer unfavorable. so 4-3x^0,2>=0,2 or 4>=3x^0,2 or 4/3>= x^0,2 or -?(4/3)<=x<=?(4/3) that's the area. the form could then be [93e7709cfdece731b854c055e03e856593e7709cfdece731b854c055e03e856593e7709cfdece731b854c055e03e8565] the two values 0,2 and 0,2 are inclusive that's indicated by making use of sq. brackets. consequence is 0 while x^0,2=4/3 consequence is 0,2 while x=0,2 different values are that are in-between additionally are blanketed