Question

Dada a função f : R⇒R definida por f(x) = x² + 1, faça o que se pede:
a) calcule x tal que f(x) = 10
b) calcule f(5√2) - f(0) / f(-2)

Answer 1

Função f(x) = x² + 1

a) f(x) = 10
x² + 1 = 10 (substitui o f(x) pelo 10)
x² = 9
x = √9
x = 3

b) f(5√2) = (5√2)² + 1
f(5√2) = 5².(√2)² + 1
f(5√2) = 25 . 2 + 1
f(5√2) = 50 + 1
f(5√2) = 51

f(0) = 0² + 1
f(0) = 1

f(-2) = (-2)² + 1
f(-2) = 4 + 1
f(-2) = 5

f(5√2) - f(0) / f(-2)
51 - 1 / 5
50 / 5 = 10

Answer 2

f(x) = x² + 1
a) calcule x tal que f(x) = 10

x^2 + 1 = 10 ==> x^2 = 10-1 ==> x^2 = 9 ==> x = +/- 3

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b) calcule f(5√2) - f(0)
                            f(-2)

f(5√2) =  (5V2)^2 + 1 ==> 25.2 + 1 ==> 50+1==> 51

f(0) = 0^2 + 1 ==> 0+1 ==> 1

 f(-2) = (-2)^2 + 1 ==> 4 +1==> 5

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b) 

f(5√2) - f(0) =  51 - 1 ==> 255 - 1 ==> 254
            f(-2)            5             5              5