Given the functions #f(x)=x^2 -4# and #g(x)= 2x -3#, how do you find the positive interval of unity length, in which these two functions intersect?

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Answer 1 · 2018-07-02T21:08:48

Two given functions #f(x)=x^2-4# & #g(x)=2x-3# will intersect each other where #f(x)=g(x)#

#x^2-4=2x-3#

#x^2-2x-1=0#

#x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-1)}}{2(1)}#

#x=1\pm\sqrt2#

#g(1+\sqrt2)=2(1+\sqrt2)-3=2\sqrt2-1#

#g(1-\sqrt2)=2(1-\sqrt2)-3=-2\sqrt2-1#

The functions intersect each other at two points #(\sqrt2+1, 2\sqrt2-1)# & #(-\sqrt2+1, -2\sqrt2-1)#