Exercise 97 Page 259

We want to find the inverse of the equation y=3x-2. To do this we will first switch x and y in the equation. y=3x-2 ⇔ x=3y-2 The next step is to solve this equation for y.

x=3y-2

AddEqn

LHS+2=RHS+2

x+2=3y

DivEqn

.LHS /3.=.RHS /3.

x+2/3=y

RearrangeEqn

Rearrange equation

y=x+2/3

The equation of the inverse is y= x+23.

We have been asked to find the inverse of y= x+14. Let's first switch x and y in the equation. y= x+14 ⇔ x= y+14 We will now solve this equation for y.

x= y+14

MultEqn

LHS * 4=RHS* 4

4x=y+1

SubEqn

LHS-1=RHS-1

4x-1=y

RearrangeEqn

Rearrange equation

y=4x-1

We have found the equation of the inverse, y=4x-1.

The first step in finding an inverse to a function is to switch x and y. Let's do that for y=x^3+1. y=x^3+1 ⇔ x=y^3+1 The next step is to solve the equation for y.

x=y^3+1

SubEqn

LHS-1=RHS-1

x-1=y^3

RadicalEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x-1)=y

RearrangeEqn

Rearrange equation

y=sqrt(x-1)

We are now finished, and the equation of the inverse is y=sqrt(x-1).