Question

Part 1.] Which of the following is the inverse of the given function?
$y= 3 x^{5}-4$
A.] $y= \sqrt[5]{ \frac{x+3}{4}}$
B.] $y= \sqrt[5]{ \frac{x-4}{3}}$
C.] $y= \sqrt[3]{ \frac{x+4}{5}}$
D.] $y= \sqrt[5]{ \frac{x+4}{3}}$

Part 2.] What is the inverse of the function $y=3 e^{-4+1}$?
A.] $y= \frac{1-log(x-3)}{4}$
B.] $y= \frac{1-log( \frac{x}{3})}{4}$
C.] $y= \frac{1-ln(x-3)}{4}$
D.] $y= \frac{1-ln( \frac{x}{3})}{4}$

Answer 1

1. I believe the answer is D, y = fifth root of (x+4)/3
y = 3x⁵ - 4
Interchanging x and y
x = 3y⁵ - 4
solving for y in the equation; x=3y⁵-4
y = ((x+4)/3)^1/5

= ((x+4)/3)^1/5

2. inverse of the equation y = 3e^-4x+1
I think the answer is D; 
Interchanging the variables x and y 
 x= 3e^-4y-1
Solving for y in x = 3e^-4y +1
y= -(In(x/3)-1)/4
  = (1-In(x/3))/4