The general solution to the differential equation 𝑑𝑦𝑑𝑥=𝑥𝑦 is 𝑦=±𝑥2+𝐶. Let 𝑦=𝑓(𝑥) be the particular solution to the differential equation with the initial condition 𝑓(−2)=−2. Which of the following is an expression for 𝑓(𝑥) and the domain for which the solution is valid?

The solution to the ordinary differential equation y˙(t)=−2y(t),y(0)=1,𝑦˙(𝑡)=−2𝑦(𝑡),𝑦(0)=1, isy(t)=−2e−2t𝑦(𝑡)=−2𝑒−2𝑡y(t)=2e−2t𝑦(𝑡)=2𝑒−2𝑡y(t)=e−2t𝑦(𝑡)=𝑒−2𝑡y(t)=−e−2t

Given a function: 𝑓(𝑥) = 𝑥2 + 2.a. Does 𝑓(𝑥) has an inverse for all values of 𝑥.b. Find a possible largest domain where 𝑓(𝑥) has an inverse. Then find the inversefunction 𝑓−1(𝑥).c. What is the domain and range of 𝑓−1(𝑥)

What is domain of function 𝑓(𝑥)=𝑥12?

Determine the domain of the functiony=|x+2|−1𝑦=|𝑥+2|−1.Select one:A.x⩾−7𝑥⩾−7B.y⩾−1𝑦⩾−1C.y∈R𝑦∈𝑅D.x∈R

Instructions: y𝑦 varies directly with x𝑥. If y=−4𝑦=−4 when x=2𝑥=2, find y𝑦 when x=−6𝑥=−6. State the equation. Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12−12). Equation: y=𝑦= Solution: y=