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Solution

f(x) = x² + 6x + 7

g(x) = 7

At point of intersection f(x) = g(x)

==> x² + 6x + 7 = 7

==> x² + 6x = 0

==> x(x + 6) = 0

==> x = 0 , x + 6 = 0

==> x = 0 , x = -6

Hence points of intersection of f(x) and g(x) are (0 , 7) and (0 , -6)