Question

Find the inverse of the following functions f(x)=6-3x g(x)=x+2

Answer 1

Problem 1:


`y=f\left( x \right) ,\\ \\ y=6-3x\\ \\ 3x=6-y\\ \\ x=\frac { 6 }{ 3 } -\frac { y }{ 3 } \\ \\ x=2-\frac { 1 }{ 3 } y\\ \\ \therefore \quad { f }^( -1 )\left( x \right) =2-\frac { 1 }{ 3 } x`

Problem 2:


`y=g\left( x \right) ,\\ \\ y=x+2\\ \\ x=y-2\\ \\ \therefore \quad { g }^( -1 )\left( x \right) =x-2`

Answer 2

f(x) = -3x + 6
y = -3x + 6
x = -3y + 6
x - 6 = -3y
-3 -3
⁻¹/₃x + 2 = y
⁻¹/₃x + 2 = f⁻¹(x)

g(x) = x + 2
y = x + 2
x = y + 2
x - 2 = y
x - 2 = g⁻¹(x)