Algebra, Trig Given F (X) = -3X

Algebra, Trig

Given f (x) = -3x + 2 and g (x) = 2x + 9: find (g 0 f)(x)

(g 0 f)(x) = 2(-3x + 2) + 9 = -6x + 4 + 9 = -6x + 13

(g 0 f)(x) = -6x + 13.

Given f (x) = 5x + 7 and g (x) = 5x -- 1: find (f 0 g)(x)

(f 0 g)(x) = 5(5x -- 1) + 7 = 25x -- 5 + 7 = 25x +

(f 0 g)(x) = 25x + 2.

Given f (x) = 5x + 4 and g (x) = 3x -- 8, find fg = f (x) * g (x) = (5x + 4)(3x -- 8) = 15x^2 -- 40x + 12x -- 32 = 15x^2 -- 28x --

fg = 15x^2 -- 28x -- 32.

Given f (x) = 2 -- 2x and g (x) = -6x + 2, find f + g f + g = f (x) + g (x) = (2 -- 2x) + (-6x + 2) = 2 -- 2x -- 6x + 2 = -8x +

f + g = -8x + 4.

Find the center and the radius of a circle, given the following equation of the circle: x^2 + y^2 + 100

The standard equation of a circle is the following: (x -- h)^2 + (y -- k)^2 = r^2, where the center is (h, k). The above equation can be re-written as follows:

(x -- 0)^2 + (y -- 0)^2 = 100, where (h, k) is (0, 0), and r^2 = 100 = 10^2, r = 10.

Answer: For x^2 + y^2 + 100, the center (h, k) = (0, 0), and the radius r = 10.

6. Find the midpoint of the line segment with the given end points: (2,1) and (6,8)

The midpoint formula is the following: midpoint = ([(x1 + x2) / 2], [(y1 + y2) / 2])

(x1, y1) = (2, 1) and (x2, y2) = (6, 8)

Therefore ([(2 + 6) / 2], [(1 + 8) / 2]) = (8/2, 9/2) = (4, 9/2) or (4, 4.5)

Answer: The midpoint of the line segment is at (4, 9/2) or (4, 4.5).

7. Given f (x) = 8x -- 2 and g (x) = 2x -- 3, find f -- g f -- g = f (x) -- g (x) = (8x -- 2) -- (2x -- 3) = 8x -- 2 -- 2x + 3 = 6x + 1

Answer: f -- g = 6x + 1.

8. Write the standard form of the equation of the circle with the given center (-2, -4) and radius 6

The standard form of a circle is the following equation: (x -- h)^2 + (y -- k)^2 = r^2, where (h, k) is the center.

r = 6, (h, k) = (-2, -4), therefore the equation becomes (x -- (-2))^2 + (y -- (-4))^2 = 6^2, which equals (x + 2)^2 + (y + 4)^2 = 36.

Answer: Standard form of circle is (x + 2)^2 + (y + 4)^2 = 36.

9. Find the distance between the pair of points: (-2,-6) and (7, -3)

Use the distance formula: d = sqrt[ (x2 -- x1)^2 + (y2 -- y1)^2 ]