Question

(Please show work on paper) Solve for inverse functions.

a) (y = sqrt{x+3})
b) (y = {1}/{2}(x-4))
c) (y = 3x^2 - 2)
d) (y = e^{2x})

Answer 1

To solve for inverse functions, swap the x and y variables and solve for y. For each given equation, we find the inverse function by following this process.

Step-by-step explanation:

To solve for inverse functions, we need to swap the x and y variables and solve for y. Let's go through each part:

a) For y = sqrt(x+3), swap x and y to get x = sqrt(y+3). To solve for y, square both sides and subtract 3 to get y = x^2 - 3.

b) For y = (1/2)(x-4), swap x and y to get x = (1/2)(y-4). Solve for y by multiplying both sides by 2 and adding 4 to get y = 2x + 4.

c) For y = 3x^2 - 2, swap x and y to get x = 3y^2 - 2. This is not a function because it is a quadratic equation, not a linear equation.

d) For y = e^(2x), swap x and y to get x = e^(2y). To solve for y, take the natural logarithm (ln) of both sides to get ln(x) = 2y. Divide both sides by 2 to get y = (1/2)ln(x).