Given the functions:g(x) = x - 2h(x) = x2 + 4x - 4f(x) = 2x + 3Determine the following functions:a. (f + g)(x)b. (f - g)(x)c. (f +h)(2)d. (fºg)(x)e.[tex] \frac{h \: (x)}{g \: (x)} [/tex]. Created by cobesarahquintas. Math

Answer:Step-by-step explanation:Given:

tex]...

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Answer:

$\green{ \boxed{a. \: (f + g)(x) = 3x + 1}}$

$\green{ \boxed{b. \:( f - g)(x) = x + 5}}$

$\green{ \boxed{c. \: (f + h)(2) = 15}}$

$\green{ \boxed{d. \:(fog)(x) = 2x - 1}}$

$\green{ \boxed{e. \: \frac{h(x)}{g(x} = \frac{ {x}^{2} + 4x - 4 }{x - 2} }}$

Step-by-step explanation:

Given:

$\purple{g(x) = x - 2}$

$\purple{h(x) = {x}^{2} + 4x - 4}$

$\purple{f(x) = 2x + 3}$

$a. \: (f + g)(x) = f(x) + g(x) \\ (f + g)(x) = (2x + 3) + (x - 2) \\ (f + g)(x) = 2x + 3 + x - 2 \\ (f + g)(x) = 2x + x + 3 - 2 \\ \green{ \boxed{(f + g)(x) = 3x + 1}}$

$b. \: (f - g)(x) = f(x) - g(x) \\ (f - g)(x) = (2x + 3) - (x - 2) \\ (f - g)(x) = 2x + 3 - x + 2 \\ (f - g)(x) = 2x - x + 3 + 2 \\ \green{ \boxed{(f - g)(x) = x + 5}}$

$c. \: (f + h)(x) = f(x) + h(x) \\ (f + h)(x) =(2x + 3) + ( {x}^{2} + 4x - 4) \\ (f + h)(2) =(2(2) + 3) + ( {2}^{2} + 4(2) - 4) \\ (f + h)(2) =(4 + 3) + (4 + 8 - 4) \\ (f + h)(2) =7 + 8 \\ \green{ \boxed{(f + h)(2) =15}}$

$d. \: (fog)(x) = f(g(x)) \\ (fog)(x) = 2x + 3 \\ (fog)(x) = 2(x - 2) + 3 \\ (fog)(x) = 2(x) + 2( - 2) + 3\\ (fog)(x) = 2x - 4 + 3 \\ \green{ \boxed{(fog)(x) = 2x - 1}}$