Blog: Find the inverse of g(x)=-2x+4

Find the inverse of g(x)=-2x+4

Hello!

The inverse function $\displaystyle{{g}}^{{-{1}}}{\left({y}\right)}$ is a function such that $\displaystyle{g{{\left({{g}}^{{-{1}}}{\left({y}\right)}\right)}}}$ = y and $\displaystyle{{g}}^{{-{1}}}{\left({g{{\left({x}\right)}}}\right)}={x}.$ To find it, we need to solve for x the equation

$\displaystyle{g{{\left({x}\right)}}}={y},$ in this case it is $\displaystyle-{2}{x}+{4}={y}.$

It is simple: $\displaystyle-{2}{x}={y}-{4},$ $\displaystyle{2}{x}=-{y}+{4},$ $\displaystyle{x}=-\frac{{1}}{{2}}{y}+{2}.$ You can check the above equalities from the definition of an inverse function.

The answer: the inverse function is $\displaystyle{{g}}^{{-{1}}}{\left({y}\right)}=\ldots$

Hello!

The inverse function $\displaystyle{{g}}^{{-{1}}}{\left({y}\right)}$ is a function such that $\displaystyle{g{{\left({{g}}^{{-{1}}}{\left({y}\right)}\right)}}}$ = y and $\displaystyle{{g}}^{{-{1}}}{\left({g{{\left({x}\right)}}}\right)}={x}.$ To find it, we need to solve for x the equation

$\displaystyle{g{{\left({x}\right)}}}={y},$ in this case it is $\displaystyle-{2}{x}+{4}={y}.$

It is simple: $\displaystyle-{2}{x}={y}-{4},$ $\displaystyle{2}{x}=-{y}+{4},$ $\displaystyle{x}=-\frac{{1}}{{2}}{y}+{2}.$ You can check the above equalities from the definition of an inverse function.

The answer: the inverse function is $\displaystyle{{g}}^{{-{1}}}{\left({y}\right)}=-\frac{{1}}{{2}}{y}+{2}.$

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