The one-to-one functions g and h are defined as follows. g={(-8, -4), (-3, 6), (1, 9), (2, 1)} h(x) = 3x+13 Find the following. - 1 g`¹ (1) h' (t)- 1 on) (-6) <-1 = = 9 X 3 13 0|0 X Ś

and g(x) = 2x¹ + 5x - 1. 3. Let f(x) = x¹/3 and g(x) A. Write out the equations for all four functions: ƒ(x), ƒ'(x), g(x), and g'(x). B. In each of the following, combine the functions f, f', g, and g' as given to write and simplify a function of x. 1. f(g(x)) II. f' (g(x)).g'(x) III. g(f(x)) IV._g(f(x))• f'(x)

Suppose that the functions p and g are defined as follows. p (x) =-5x-2 q (x)=5x+3 Find the following. (4 °p)(3) = [] (p •q)(3) = ] ?

find f ′(x) for each function. f (x) = x4 + 2/x

Imagine that we can quarantine infected members of the population, so that they are unable to transmit the disease to others. Let q represent the fraction of the infected population which is quarantined, and let 1-q represent the fraction of the infected population that is not quarantined and can transmit the disease to the susceptible individuals. (Please use google sheets) a. Rewrite the difference equation for S[t+1] and I[t+1] (from question 1), to incorporate the effects of quarantine. (Hint: quarantine should affect the term representing the proportion of susceptible individuals who are interacting with infected each time step) b. In the model you developed for question 1 implement the fraction of quarantined people by adding  (1-q) to the equations for S and I. Show what happens for a quarantine percentage of 50%, meaning that 50% of infectious people are in quarantine and cannot interact with the susceptible. What can you tell about the impact of quarantine.

If y = 5(1 - e-2x), compute y and show that y = 10 - 2y.

Eliminate the arbitrary constant on the given equation y=( C1+C2x) e2x+ex

Find the inverses of y=(1-e-x)/(1+e-x).

Which of the following Functions are inverses to each other: Vx+8 A- f(x) = (4x – 3)', g(x) = 7. B- f(x) = Vx+ 3- 5, g(x) = (x + 3)³ + 5 C- f(x) = " - 9, g(x) =; 18 x+9 D- f(x) = 9+VI, g(x) = 9– x³

If a function h satisfies h(-x) = h(x) for every number x in its domain, then h is called an even function. If h satisfies h(-x) = -h(x) for every number x in its domain, then h is called an odd function. Suppose that sh(x) dx = Answer the following: −1 and ſ³ h(x)dx = 2 -3 A. Suppose that h is an even function. Evaluate ſ³, h(x)dx. B. Suppose that h is an odd function. Evaluate ſ³, h(x)dx. C. Evaluate (2h(x) + 1)dx. D. Evaluate fh(x + 1)dx.