Preparing for University Calculus - Math and Computer Science

Problems: (answers on page 40)1. If f(x) =1/x, find the largest possible domain (within the real numbers) onwhich f could be defined.2. If f(x) =1/(x + 1), find the domain of f.3. If g(x) =x 2 + 2, find g(1 + x)4. If f(x) =x 2 , find the range of f.5. Find the domain and range of f(x) = |x|x6. If f(x) = 1x +1 , find (a) f(x2 ); (b) f(−2); (c)f( √ x).7. If f(x) =1/x and g(x) =x 2 , find f(g(a)).8. If f(x) =1/x and g(x) =x 2 , find g(f(2)).9. If f(x) =1/(x + 1), find f(f(x))10. If f(x) =x −3 , find the inverse function.11. Which of the following functions is its own inverse:(a) f(x) =x 2 , (b) g(x) =−x, (c)h(x) =x(d) each of f,g and h (e) g and h only12. Which of the following functions has an inverse function?(a) f(x) =x 3 , (b) g(x) =x 5 , (c)h(x) =x(d) each of f,g and h (e) g and h only13. Finds the inverse of f(x) = x +12x +1 . 17