Question

Dadas as funções f(x) = x – 1; g(x) = x² + 3; h(x) = 5x² – 2x + 1, calcule: a) f(g(x)); b) g(h(x)); c) g o f; d) h o f; e) g(f(2)); f) h(g(1))

Answer 1

Resposta:

Explicação passo-a-passo:

f(x) = x – 1;

g(x) = x² + 3;

h(x) = 5x² – 2x + 1, calcule:

a) f(g(x));

f(x) = x – 1

g(x) = x² + 3

f[g(x)] = x² + 3 - 1

f[g(x)] = x² + 2

_____________

b) g(h(x));

h(x) = 5x² – 2x + 1

g(x) = x² + 3

g[h(x)] = (5x² – 2x + 1)² + 3

g[h(x)] =

(5x² – 2x + 1).(5x² – 2x + 1)+3

= 25x^4 - 10x^3 + 5x^2 - 10x^3 + 4x^2 - 2x + 5x^2 - 2x + 1 + 3

= 25x^4 - 20x^3 + 14x^2 - 4x + 4

________

c) g o f;

g(x) = x² + 3

f(x) = x – 1

G o f = (x-1)² + 3

G o f = x² - 2x + 1 + 3

G o f = x² - 2x + 4

---------------

d) h o f;

h(x) = 5x² – 2x + 1

f(x) = x – 1

H o f = 5.(x-1)² – 2.(x-1) + 1

H o f = 5.(x² – 2x + 1) - 2x + 2 + 1

H o f = 5x² – 10x + 5 - 2x + 3

H o f = 5x² – 12x + 8

---------------

e) g(f(2));

f(x) = x – 1

g(x) = x² + 3

g [f(x)] = (x-1)² + 3

g[f(2)] = (2-1)² + 3

g[f(2)] = 1+3

g[f(2)] = 4

____________

f) h(g(1))

g(x) = x² + 3;

h(x) = 5x² – 2x + 1

h[g(x)] = 5x² – 2x + 1

h[g(x)] = 5.(x² + 3)² – 2.(x² + 3) + 1

h[g(1)] = 5.(1² + 3)² - 2.(1² + 3) + 1

h[g(1)] = 5.(1+3)² - 2.(1+3) + 1

h[g(1)] = 5.(4)² - 2.4 + 1

h[g(1)] = 5.16 - 8 + 1

h[g(1)] = 80 - 7

h[g(1)] = 73