1. Your approach would normally work, except that the function has a discontinuity at x = 1. But what is the limit of the function? Factor the numerator to yield . Then cancel the factors of and you are left with . At x = 1, this function is equal to 14, so the limit is 14, and that is the function value you want for the other part of your function.
2. Substitute , yielding . Then solve for u by factoring and identifying the roots: , so u = 1 or 6. Hence or . From you have the solution x = 0, and from you have the solution x = ln 6.
3. This is an easy one. The equation can be rewritten as . With (28, 1) on the graph, we have , or .
4. You can combine the two logarithms to yield , which can be written , or . Now apply the quadratic formula: . Recognizing that x must be a positive number in order to evaluate the logarithm, we have .