Question

Let f(x)=2x-6. solve f^-1(x) when x=2.

Answer 1

a) Calculating f⁻¹(x)


`y=2x-6\\ \\ x=2y-6\\ \\ 2y=x+6\\ \\ y=(x+6)/(2)\\ \\ \boxed{f^(-1)(x)=(x+6)/(2)}`

b) Calculating f⁻¹(2)


`\boxed{\boxed{f^(-1)(2)=(2+6)/(2)=(8)/(2)=4}}`

Answer 2

`f(x)=2x-6\\ y=2x-6\\ 2x=y+6\\ x=(1)/(2)y+3\\ f^(-1)(x)=(1)/(2)x+3\\ f^(-1)(2)=(1)/(2)\cdot2+3\\ f^(-1)(2)=1+3\\ f^(-1)(2)=4`