Find the inverse of each function
1) g (x)= 3+(x-1)^3
4) f (x)=x^3+2
5) f (n)= 5 square root of (-n+1/2)

To find the inverse
1. replace f(x) or g(x) or f(n) with y
2. switch places of x and y
3. solve for y
4. replace y with f⁻¹(x) or g⁻¹(x) or f⁻¹(n)

1.
g(x)=3+(x-1)^3
replace
y=3+(x-1)^3
switch
x=3+(y-1)^3
solve
x=3+(y-1)^3
subtract 3
x-3=(y-1)^3
cube root both sides
=y-1
add 1
+1=y
switch y with g⁻¹(x)
g⁻¹(x)=+1

4. f(x)=x^3+2
replace with y
y=x^3+2
switch x and y
x=y^3+2
solve for y
x=y^3+2
subtract 2
x-2=y^3
cube roo both sides
=y
replace with f⁻¹(x)
f⁻¹(x)=

5.
f(n)=5
replace
y=5
switch n and y
n=5
solve for y
n=5
divide both sides by 5
n/5=n=
square both sides
=-y+1/2
subtract 1/2 from both sides
-=-y
multiply both sides by -1
-+=y
replace with f⁻¹(n)
f⁻¹(n)=-+

1.  g⁻¹(x)=+1
4.  f⁻¹(x)=
5.  f⁻¹(n)=-+