What is the inverse of the function? g(x)=−4/3x +2

Dec 10, 2017

${g}^{-} 1 \left(x\right) = - \frac{3}{4} x + \frac{3}{2}$

This is the first selection.

Explanation:

Given:

g(x)=−4/3x +2

Substitute ${g}^{-} 1 \left(x\right)$ for every instance of x:

g(g^-1(x))=−4/3g^-1(x) +2

We know that one of the properties of a function and its inverse is, $g \left({g}^{-} 1 \left(x\right)\right) = x$, therefore, the left side becomes x:

x=−4/3g^-1(x) +2

Solve for ${g}^{-} 1 \left(x\right)$:

−4/3g^-1(x) +2 = x

−4/3g^-1(x) = x -2

${g}^{-} 1 \left(x\right) = - \frac{3}{4} x + \frac{3}{2}$

This is the first selection.