For fx Squareroot x 4 and gx 1x 8 what is the domain of

For f(x) = Squareroot x - 4 and g(x) = 1/x - 8 what is the domain of (f middot g)(x)? A) (4, 8) (8, infinity) B) [4, infinity] C)[4, 8) (8, infinity) D) [0, 8) (8, infinity) Find the requested composition of functions. Given f(x) = 5/x - 6 and g(x) = 3/7x find (f degree g)(x) a) 35x/3 + 42x B) 5x/3- 42x C) 3x - 18/35x D) 35x/3 - 42x Find the requested function value. Find (h degree g degree f)(-9) when f(x) = x - 3/4, g(x) = 7 - x^2, and h(x) = |x - 9| A)-11 B) -7 C) -137 D)11 Find functions f and g so that F(x) = (f degree g) (x). F(x) = (-9x + 7)^4 A) f(x) = -9x + 7, g(x) = x^4 B) f(x) = x^4 g(x) = -9x + 7^C) f(x) = -9x^4 g(x) = x + 7 D) f(x) = (-9x)^4, g(x) = 7

Solution

3) If f(x) = (x-4) and g(x) = 1/(x-8), then (f.g)(x) = f(x) . g(x) = [(x-4)/ (x-8)]The domain of (f.g)(x) is { x R: 4 x <8} or x > 8 as the square root of a negative number is not a real number and division by 0 is not defined. In interval notation, the domain of (f. g)(x) is [4,8) U ( 8,). Option C is the correct answer.

4) If f(x) = 5/(x-6) and g(x) = 3/7x, then (f o g)(x) = f ( g(x)) = f( 3/7x) = 5/[ (3/7x)-6] = 5/[(3-42x)/7x] = 35x/(3-42x). Option D is the correct answer.

5) If f(x) = (x-3)/4, g(x) = 7-x² and h(x) = |x-9|, then (h o g o f)(x) = (h o g (f(x)) = hog [(x-3)/4] = h( g((x-3)/4 )) = h [7-(x-3)²/16)]= h [ (112-(x-3)²/16 ] = |[(112-(x-3)²/16] –(9)|=|[ -32 –(x-3)²]/16|. Hence (h o g o f)(-9) = |(-32-( -12)² /16 = | = |- 176/16| =11. Option D is the correct answer.

6) Option B is the correct answer. IUf f(x) = x⁴ and g(x) = (-9x+7), then (f o g)(x) = f ( g(x)) = f(-9x+7) =       (-9x+7)⁴ = F(x).