How can you show that there is a real number x such that cosx=x-1?

let f(x) = cos (x) - x +1

f(0) = cos(0) - 0 +1 = 2

f(pi/2) = cos(pi/2) - pi/2 + 1 = 0 - 3.14 +1 = -2.14

Since f(0) > 0 > f(pi/2)

then by the Intermediate Value Thm there is a

real number c such that f(c) = 0

or cos (c) - c+1 =0

or cos(c) = c -1

So we have proved that there is a real number x such that cosx=x-1

Show that the line f(x) = x - 1 intersects the graph of g(x) = cos(x).

Or show that h(x) = cos(x) - x + 1 has both positive and negative values.