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show that y=2^x and y=3-2x have a x coordinate between 0 and 1

f(x)= 2^x+2x-3 ( this is the step I dont understand... Why can i set f(x) to 0 and how does finding the roots of this new equation equate to intersection of the 2 equations. Any advice would be appreciated)
f(1)=1 f(x) is continuous and change of sign so x coordinate must lie in the interval (0,1)

I mostly get this problem but that one step is something I dont fully understand
combining 2 equations, equating to 0 and finding the solutions for x to that problem will give you the points of intersection.

when you make a single equation = to 0 to find the roots, imagine it as having your equation and the line y=0, and equating your equation to the line y=0 to find the roots.

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