See attached document.

See attached document.

Use the given pair of functions to find the following values if they exist. (Hint: Please see section 5.1 of the ebook) (g ◦ f)(0) (f ◦ g)(−1) (g ◦ f)(−3) (f ◦ g) (-2) (f ◦ f)(−2) Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. (Hint: Please see section 5.1 of the ebook) (g ◦ f)(x) (f ◦ g)(x) (f ◦ f)(x) Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f inverse and vice-versa. (Hint: Please see section 5.2 of the ebook) Show that the given function is one-to-one and find its inverse. Check your answers algebraically and graphically. Verify that the range of f is the domain of f inverse and vice-versa. (Hint: Please see section 5.2 of the ebook) Analytically show that the function is one-to-one, find its inverse, and evaluate the following: (Hint: Please see section 5.2 of the ebook) Rationalize the denominator, and simplify. (Hint: Please see section 0.9 of the ebook, exercise number 30, and page 120 in Section 0.9) Solve the equation (Hint: Please see section 5.3 of the ebook, exercise numbers 22 and 23) (This means x raised to the power of 3/2 is equal to 27) Find the inverse of the function from the ‘procedural perspective’ discussed in Example 6.1.5 (Hint: Please see section 6.1 of the ebook) Find the inverse of the function from the ‘procedural perspective’ discussed in Example 6.1.5 (Hint: Please see section 6.1 of the ebook) (Hint: Please see section 6.5 of the ebook, Exponential Regression Model) The data at the right shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup. The brewing pot temperature is approximately 180º F. Time (mins) Temp ( º F) 179.5 168.7 158.1 149.2 14 141.7 16 134.6 20 125.4 23 123.5 25 116.3 27 113.2 30 109.1 33 105.7 38 102.2 40 100.5 a) Find an exponential regression model of the form y = a * b^x to represent the above date, where x is the number of minutes, and y is the temperature of the cup of coffee b.) Graph the exponential regression model. c.) Decide whether the model is a “good fit” to represent this data. d) When is the coffee at a temperature of 92 degrees? e.) What is the predicted temperature of the cup of coffee after 50 minutes?

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