SOLUTION: Sketch a graph of a function f that satisfies the following conditions: f does NOT have an inverse function f(x) > x for all x f(1)

SOLUTION: Sketch a graph of a function f that satisfies the following conditions: f does NOT have an inverse function f(x) > x for all x f(1) > 0

Question 1037247: Sketch a graph of a function f that satisfies the following conditions:
f does NOT have an inverse function
f(x) > x for all x
f(1) > 0
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let .
f has no inverse function since it fails the horizontal line test for one-to-one-ness.
f(x) > x since, for all real x, , hence .
Finally f(1) = 3 > 0.
.
(Notice that the parabola is entirely above the line y = x, which signifies f(x) > x for all x.)
There still many more functions that would satisfy the initial conditions.
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