ANSWER ALL THE QUESTIONS. read carefully. INCLUDE DRAWN GRAPHS WHEN NEEDED. include all steps.

CALCULUS 1000A FW23 - Homework Assignment #1 Due: October 6th at 11:59pm (EDT) on gradescope.ca For lull credit, ensure you show all your work and explain your reasoning. Simply stating the final answer for any of the following questions will not result in full credit. You should avoid using calculators and leave your answers in exact form, even in questions involving words like \"approximately" you won't increase your grade by showing us the decimal expansion of your results, so don't worry about that extra step. Make sure you read and follow the submission instructions for Gradescope. 1. (6 marks) Forg(.r) = ln(l 12) and f(J:) = VI + 3! determine the subset of the domain of g on which the composition f o g is well-dened. What is the domain of g o J"? Find formulas for (f o g)(:r) and (9 \"(I)- 5. (3 marks + 1 bonus mark) If (a) (1 mark) What is the domain of g(:r)? (b) (1 mark) Verify (with a sketch and/or short argument) that g is a one-to-one function. (c) (1 mark) Find a formula for the inverse function: that is, nd 94(1). ((1) (1 bonus mark) Find the range of g. 6. (5 marks) Sketch the graph of a function f with the following properties: I I is not continuous when 1: = 2 but \"mat>2 \"1) exists. 0 f has a jump discontinuity when r = l. o f is continuous at all points other than where I = 2 or .1: = 1