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Fiesta28 [93]
3 years ago
14

Let ƒ(x) = 5x − 4 and g(x) = x2 - 1. Find (ƒ ○ g)(2).

Mathematics
1 answer:
PolarNik [594]3 years ago
4 0

(f ○g ) (2)= 11

Step-by-step explanation:

(f ○g ) (x)= (f(g(x))

= 5( x² -1) – 4

= 5x² – 5 – 4

= 5x² – 9

(f ○g ) (2)= (f(g(2)) = 5 (2)² – 9 = 5(4) – 9 = 20 – 9 = 11

I hope I helped you^_^

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2 years ago
A parabola can be drawn given a focus of (5, -3) and a directrix of y=1. Write the equation of the parabola in any form.
Anna71 [15]

Answer:

(x²-10x+33)/(-8) = y

Step-by-step explanation:

The distance between any point on a parabola from both its focus and directrix are the same.

Let's say we have a point (x,y) on the parabola. We can then say that using the distance formula,

\sqrt{(x-5)^2+(y-(-3))^2}is the distance between (x,y) and the focus. Similarly, the distance between (x,y) and the directrix is |y-1| (I use absolute value here because distance is always positive). We can find this equation by taking the shortest distance from the point to the line. Because the closest point to the line will be the same x value as the point itself, the distance is simply the distance between the y value of the point and the y value of the directrix.

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Answer:

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