Step-by-step explanation:
x^2 + 4x + 8 = (x^2 + 4x + 4) + 4 = (x + 2)^2 + 4.
When x^2 + 4x + 8 > 5, this means (x + 2)^2 + 4 > 5.
So (x + 2)^2 > 1.
=> (x + 2) > 1 or (x + 2) < -1.
=> x > -1 or x < -3.
She does 414,829.24324324 per minute.
184,184,184÷444= 414,829.24324324
h(x) = x g(x)
h'(x) = x g'(x) + (1)g(x)
h'(x) = x g'(x) + g(x)
Since g(x) = f^-1(x), then
g'(x) = 1/f'(x)
h'(x) = x/f'(x) + f^-1(x)
Therefore,
h'(5) = 5/f'(5) + f^-1(5).
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