# How do you graph g(x)=5x and g^-1(x) on the same set of axes?

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The graph of the function g(x) = 5x is the line y = g(x) = 5x.

To determine the inverse of g(x) let y = g(x) = 5x. Now isolate x

=> x = y/5

Interchange x and y

=> y = x/5

=> `g^-1(x) = x/5`

The graph of the inverse function is y = x/5.

The graph of the functions has been plotted below, the function g(x) = 5x is in red and its inverse is in green

For g(x), its is simply a line with a slope of 5, that has a y intercept of 0. For every x value, multiply by 5 for the coresponding y value. For its inverse, g^-1(x), simply interchange the the domain (x values) and range (y values) with each other. This is essentially just making it 1/5x.