Question

in exercises 1–4, find ((f + g)(x)) and ((f - g)(x))
then evaluate (f + g) and (f - g) for the given value of (x).

1. (f(x) = -\frac{1}{2}sqrt3{x}, g(x) = \frac{9}{2}sqrt3{x}; x = -1000)
2. (f(x) = -x^2 - 3x + 8, g(x) = 6x - 3x^2; x = -1)
3. (f(x) = 4x^3 + 12, g(x) = 2x^2 - 3x^3 + 9; x = 2)
4. (f(x) = 5sqrt4{x} + 1, g(x) = -3sqrt4{x} - 2; x = 1)

in exercises 5–8, find ((fg)(x)) and (left(\frac{f}{g}
ight)(x)) and state the doma
evaluate (fg) and (\frac{f}{g}) for the given value of (x).

1. (f(x) = -x^3, g(x) = 2sqrt3{x}; x = -64)
2. (f(x) =
3. (f(x) = 0.25x^{1/3}, g(x) = -4x^{3/2}; x = 1)
4. (f(x) =)

Explanation:

Answer:

1. $(f+g)(x) = 4\sqrt[3]{x}$, $(f-g)(x) = -5\sqrt[3]{x}$; $(f+g)(-1000) = -40$, $(f-g)(-1000) = 50$
2. $(f+g)(x) = -4x^2+3x+8$, $(f-g)(x) = 2x^2-9x+8$; $(f+g)(-1) = 1$, $(f-g)(-1) = 19$
3. $(f+g)(x) = x^3+2x^2+21$, $(f-g)(x) = 7x^3-2x^2+3$; $(f+g)(2) = 37$, $(f-g)(2) = 51$
4. $(f+g)(x) = 2\sqrt[4]{x}-1$, $(f-g)(x) = 8\sqrt[4]{x}+3$; $(f+g)(1) = 1$, $(f-g)(1) = 11$
5. $(fg)(x) = -2x^{10/3}$, $(\frac{f}{g})(x) = -\frac{1}{2}x^{8/3}$; $(fg)(-64) = -2,097,152$, $(\frac{f}{g})(-64) = -32,768$
6. $(fg)(x) = -x^{11/6}$, $(\frac{f}{g})(x) = -0.0625x^{-7/6}$; $(fg)(1) = -1$, $(\frac{f}{g})(1) = -0.0625$