Find the inverse if each of the following functions given

Question

f(x)=5x-12

g(x)=x²⁺⁸

h(x)=10x-6/11

f(x)=³√4x+12

h(x)=(x-27)³

Answer 1

y = 5x - 12

 

x = 5y - 12

 

(x+12)/5 = y

 

-------------------------------

 

y = x^10 

 

x = y^10

 

y = x^(1/10)

 

BUT IF you meant y = x^2 + 8 then

 

x = y^2 + 8

 

(x-8) = y^2

 

y = sqrt(x-8)

 

-----------------------------------

 

y = 10x - 6/11

 

x = 10y - 6/11

 

(x+6/11) = 10y

 

y = (1/10)(x + 6/11)

 

-----------------------------

 

y = cube_root(4)*x + 12

 

x = cube_root(4)*y + 12

 

(x - 12) = cube_root(4)*y

 

4^(2/3)*(X-12) = 4*y

 

y = 4^(2/3)(x-12)/4

 

BUT IF you meant y= cube_root(4x) + 12 THEN

 

x = cube_root(4y) + 12

 

(x-12) = cube_root(4y)

 

(x-12)^3 = 4y

 

y = (x-12)^3/4

 

-------------------------------

 

y = (x-27)^3

 

x = (y-27)^3

 

cube_root(x) = y - 27

 

y = cube_root(x) + 27