Step-by-step explanation:
I will do the first one as an example.
To find the inverse of y = f(x), simply switch x and y, then solve for y.
y = 3 + 2 ln x
x = 3 + 2 ln y
x − 3 = 2 ln y
(x − 3) / 2 = ln y
y = e^((x − 3) / 2)
So the inverse function is:
f⁻¹(x) = e^((x − 3) / 2)
The original function told us the amount of water as a function of time.
The inverse function tells us the time as a function of the amount of water.
Here's the given:
P=$400
i=7.5%
A=$8500
The formula used for this problem is:
A = P(1+i)^t
Manipulating the equation to arrive at t, we have:
t = ln(A/P) / ln(1+i)
Plugging in values:
t = ln($8500/$400) / ln(1+0.075)
<span>t = 42.26 years</span>
Answer:
x = ± 2
Step-by-step explanation:
Given
3x² = 12 ( divide both sides by 3 )
x² = 4 ( take the square root of both sides )
x = ± 
= ± 2
All work is shown in picture below.
