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f(x)

B. Clase 41. A. C. x. Operaciones con funciones Función compuesta. g. f. f(x). g(f(x)). g(x) = x + 1. (g – f)(x) = x + 1 – (x – 2). 1x. y h(x) =. (f + g)(x) = x – 2 + x + 1. = x + 1 – x + 2. Sean las funciones f(x) = x – 2 ;. Dom f: .

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f(x)

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  1. B Clase 41 A C x Operaciones con funciones Función compuesta g f f(x) g(f(x))

  2. g(x) = x + 1 (g – f)(x) = x + 1 – (x – 2) 1x y h(x) = (f + g)(x) = x – 2 + x + 1 = x + 1 – x + 2 Sean las funciones f(x) = x – 2 ; Dom f:  Dom g = {x  | x  –1} Dom h: * Dom (f +g) = {x| x  – 1} = Dom g Dom (g – f) = Dom g

  3. g(x) = x + 1 x +1 x + 1 1x 1x y h(x) = x + 1 = x x – 2 fg(x) = Sean las funciones f(x) = x – 2 ; Dom f:  Dom g = {x  | x  -1} Dom h: * hg(x)= Dom hg={x| x  –1, x 0} Dom fg = {x |x> –1}

  4. B A C y x z L.T. 11no. grado, pág. 184 g f y = f(x) z = g(y) = g(f(x)) (gof)(x) = g(f(x)) Función compuesta de f y g

  5. = g( x ) =  x + 4 f(x) =  x . =  x + 4 Ejemplos: Sean las funciones g(x) = x + 4 y La composición de funciones no es una operación conmutativa. Determina: a) (gof)(x) b) (fog)(x) a) (gof)(x) = g(f(x)) Dom(gof)(x) = x   | x  0 b) (fog)(x) = f(x + 4) = f(g(x)) Dom (fog)(x) = x   | x  – 4  (gof)(x)  (fog)(x)

  6. r (x) = x + 3 y t(x) =  x – 2 + 1 =r(x – 2 + 1 ) =   x – 2 + 1 + 3 =   x – 2 + 4 Ejercicio Dadas las funciones : a) Determine la función q(x) =r ot(x) q(x) =r ot(x) = r (t(x) ) Dom q:x   | x  2

  7. b) Halle, si existen,los ceros de q(x). x– 2 +4 = 0  x– 2= – 4   18 – 2 + 4 = 8 08 2 2 0=  x – 2 + 4 x – 2 = 16 x = 18 La función no tiene ceros Comprobación:

  8. y h(x) =  x – 2. Para el estudio individual Sean las funciones: f(x) = x3 + 1; 1 g(x) = x Determina: a) (gof)(x) b) (hog)(x) c) (hof)(x)

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