Question

Find the inverses of each of the functions below algebraically.

a.3y+5x=18

b.h(t)=−4.9(t+3)^2+45.8

Answer 1

3y+5x=18
two step process to find the inverse of a linear function
1. interchange the x and y variables
---> 3x + 5y = 18
2. solve the new equation for y
5y = -3x + 18
y = (-3/5)x + 18/5

since the original was in standard form, we could have left the inverse in standard form as 3x + 5y = 18

b)
let s = -4.9t^2 + 45.8
interchange the variables ...
t = -4.9s^2 + 45.8
4.9t^2 = 45.8 - t
t^2 = (45.8 - t)
t = ±√( (45.8-t)/4.9 ) --> notice that this is not a function