EJERCICIOS DE MATEMATICA: FUNCIONES

EJERCICIOS DE LA PAGINA 19

1. Considerando las siguientes funciones, calcula sus respectivas imágenes para x = -1; x = 0; x = 1; x = 1/2; x = √2

a. f : x →f(x)= 4x² + 2
b. g : x →g(x)= -2x² + 2
c. h : x →h(x)= √ 2 - 2x²

a. f: x→f(x)=4x²+2

f(-1)=4x²+2 f(0)=4x²+2 f(1)=4x²+2
f(-1)=4(-1)²+2 f(0)=4(0)²+2 f(1)=4(1)²+2

f(-1)=4(1)+2 f(0)=4(0)+2 f(1)=4(1)+2

f(-1)=4+2 f(0)=0+2 f(1)=4+2 f(-1)=6 f(0)=2 f(1)=6

f(1/2)=4x²+2 f(√2)=4x²+2
f(1/2)=4(1/2)²+2    f(√2)=4(√2)²+2
f(1/2)=4(1/4)+2   f(√2)=4(2)+2
f(1/2)=4/4+2    f(√2)=8+2
f(1/2)=1+2    f(√2)=10
f(1/2)=3

b. g : x →g(x)= -2x² + 2

  g(-1)= -2x² + 2   g(0)= -2x² + 2   g(1)= -2x² + 2
  g(-1)= -2(-1)² + 2 g(0)= -2(0)² + 2 g(1)= -2(1)² + 2
  g(-1)= -2(1) + 2 g(0)= -2(0) + 2 g(1)= -2(1) + 2
  g(-1)= -2 + 2 g(0)= 0+ 2   g(1)= -2 + 2
  g(-1)= 0   g(0)= 2   g(1)= 0

f(1/2)=-2x²+2 f(√2)=-2x²+2
f(1/2)=-2(1/2)²+2    f(√2)=-2(√2)²+2
f(1/2)=-2(1/4)+2   f(√2)=-2(2)+2
f(1/2)=-1/2+2    f(√2)=-4+2
f(1/2)=3/2    f(√2)=-2

c. h : x →h(x)= √ 2 - 2x²

  h(-1)= √ 2 - 2x²   h(0)= √ 2 - 2x²   h(1)= √ 2 - 2x²
  h(-1)= √ 2 - 2(-1)²   h(0)= √ 2 - 2(0)² h(1)= √ 2 - 2(1)²
  h(-1)= √ 2 - 2(1)   h(0)= √ 2 - 2(0) h(1)= √ 2 - 2(1)
  h(-1)= √ 2 - 2 h(0)= √ 2 -0   h(1)= √ 2 - 2
   h(0)= √ 2

  h(1/2)= √ 2 - 2x²   h(√2)= √ 2 - 2x²
  h(1/2)= √ 2 - 2(1/2)² h(√2)= √ 2 - 2(√2)²
  h(1/2)= √ 2 - 2(1/4)   h(√2)= √ 2 - 2(2)
  h(1/2)= √ 2 - 1/2 h(√2)= √ 2 -4

2. Sean las funciones siguientes, determina las anti imágenes para -1, 0, 1,√2
a. f : x →f(x)= 2x² - 2
b. f : x →f(x)= √2/3 - 4x²

a. f : x →f(x)= 2x² - 2

  f(-1)= 2x² - 2 f(0)= 2x² - 2   f(1)= 2x² - 2
  f(-1)= 2(-1)² - 2 f(0)= 2(0)² - 2   f(1)= 2(1)² - 2
  f(-1)= 2(1) - 2 f(0)= 2(0) - 2 f(1)= 2(1) - 2
  f(-1)= 2 - 2 f(0)= 0 - 2 f(1)= 2 - 2
  f(-1)= 0 f(0)= - 2 f(1)= 0

  f(√2)= 2x² - 2
  f(√2)= 2(√2)² - 2
  f(√2)= 2(2) - 2
  f(√2)= 4 - 2
  f(√2)= 2

b. f : x →f(x)= √2/3 - 4x²

  f(-1)= √2/3 - 4x² f(0)= √2/3 - 4x² f(1)= √2/3 - 4x²
  f(-1)= √2/3 - 4(-1)² f(0)= √2/3 - 4(0)² f(1)= √2/3 - 4(1)²
  f(-1)= √2/3 - 4(1)   f(0)= √2/3 - 4(0) f(1)= √2/3 - 4(1)
  f(-1)= √2/3 - 4    f(0)= √2/3 -0   f(1)= √2/3 - 4
  f(-1)= √2-12/3 f(0)= √2/3     f(1)= √2-12/3

  f(√2)= √2/3 - 4x²
f(√2)= √2/3 - 4(√2)²
    f(√2)= √2/3 - 4(2)
   f(√2)= √2/3 - 8
   f(√2)= √2-24/3

3. Representa gráficamente las siguientes funciones:

a. f : x →f(x) = -2
b. f : x →f(x) = -2x + 5

c. f: x →f(x) = x² - 2x - 3

a. f : x →f(x) = -2