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Answer:
x = -
Step-by-step explanation:
To find f(g(x)) substitute x = g(x) into f(x), that is
f(g(x))
= f(x + 1)
= 2(x + 1)² ← expand using FOIL
= 2(x² + 2x + 1) ← distribute
= 2x² + 4x + 2
To find g(f(x)) substitute x = f(x) into g(x), that is
g(f(x))
= g(2x²)
= 2x² + 1
----------------------------------------------------------
Equating gives
2x² + 4x + 2 = 2x² + 1 ( subtract 2x² + 1 from both sides )
4x + 1 = 0 ( subtract 1 from both sides )
4x = - 1 ( divide both sides by 4 )
x = -
The standard equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is
(x-h)^2 + (y-k)^2 = r^2
where the center is at point (h,k)
From the statement of the problem, it is already established that h = 2 and k = -5. What we have to determine is the value of r. This could be calculated by calculating the distance between the center and point (-2,10). The formula would be
r = square root [(x1-x2)^2 + (y1-y2)^2)]
r = square root [(2--2)^2 + (-5-10)^2)]
r = square root (241)
r^2 = 241
Thus, the equation of the circle is