1 if fx x2 2x 4 solve fx h 2 Given the following find th

1. if f(x) = -x2 + 2x - 4 solve.

f(x + h)=?

2. Given the following, find the function g.

f(x)=1/x

(f/g)(x)= x+8/x^2-x

3. Consider the following functions.

f(x) = x² + 8
g(x) = 3x² - 7

Find the following and give the domain of each.

(a) (f + g)(x) =

(b) (f - g)(x) =

(c) (fg)(x) =

(d) (f / g)(x) =

Solution

1.f(x) = -x² + 2x -4

f(x+h) = -(x+h)² + 2(x+h) -4 = -(x² + 2xh +h² ) + 2x +2h -4 = -x² - 2xh - h² + 2x +2h -4

2. f(x) = 1/x

(f/g)(x) = (x+8)/( x² -x)

(f/g)(x) = f(x)/g(x)

(x+8)/(x( x -1) )         = 1/x/g(x)

g(x) = (x-1)/(x+8)

3. f(x) = x² +8

g(x) = 3x² -7

(f+g)(x) = f(x) +g(x) = x² +8+3x² -7 =4x² +1

(f - g)(x) = f(x) - g(x) = x² +8- 3x² + 7 = -2x² + 15

(fg)(x) =f(x) *g(x) = (x² +8)(3x² -7) = 3x⁴ - 7x² + 24x² - 56 = 3x⁴ + 17 x² - 56

(f / g)(x) = f(x)/g(x) = (x² +8)/(3x² -7)