Please help Show that the inverse of a linear function y=mx+b, where m≠0 and x≠b, is also a linear function

The inverse function is:

Since and , it is a linear function with slope and intercept .

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In which:

Since and , it is a linear function with slope and intercept .

A similar problem is given at link

Let f(x) = mx+b. Also, let g(x) be the inverse of f(x)

To find the inverse, we start with y = mx+b and swap x and y. From there, we solve for y like so

y = mx+b

x = my + b

x-b = my

my = x-b

y = (x-b)/m ... note m is in the denominator, so m cannot be 0

y = (x/m) - (b/m)

y = (1/m)x - (b/m)

g(x) = (1/m)x - (b/m)

This new equation is linear because it is in the form (slope)x+(y intercept)

The new slope is 1/m and the new y intercept is -b/m

So this proves that the inverse g(x) is linear when f(x) is linear.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: