Question

A function is defined as shown.f(x)=−3x+4What is the inverse of f(x)?A. f^−1(x)=−1/3x−4/3B. f − 1 ( x ) = − 1/3 x − 4 C. f^−1(x)=−1/3x+4/3D. f ^− 1 ( x ) = − 1/3x +4

Answer 1

We need to find the inverse function of:

`f\mleft(x\mright)=−3x+4`

In order to do so, we can:

• replace x with y;

,

• replace f(x) with x;

,

• isolate y on the left side;

,

• replace y with f⁻¹(x).

We obtain:

`\begin{gathered} x=-3y+4 \\ \\ x+3y=-3y+4+3y \\ \\ 3y+x=4 \\ \\ 3y+x-x=4-x \\ \\ 3y=4-x \\ \\ (3)/(3)y=(4-x)/(3) \\ \\ y=-(1)/(3)x+(4)/(3) \\ \\ f^(-1)\left(x\right)=-(1)/(3)x+(4)/(3) \end{gathered}`

Answer: option C

`f^(-1)(x)=-(1)/(3)x+(4)/(3)`