Find the invariant point(s) algebraically between the given function and its reciprocal function.

Question

y = 1/2x+7

Answer 1

If you mean: when is 1/(2x+7) = (2x+7)/1, then

(2x+7)² = 1

4x² + 28x + 48 = 0

x² + 7x + 12 = 0

(x+3)(x+4) = 0

x = -3 or -4

When x = -3, 1/(2x+7) = 1 and when x = -4, 1/(2x+7) = -1

The points are (-3,1) and (-4,-1)