Question

Sea la función f definida por la regla f(x)=2x2-x4 Encuentre: a. f(a) b. f(a+1) c. f (a2 ) d. f (-2/3)

Answer 1

PREGUNTA

Sea la función f definida por la regla f(x)=2x^2-x^4

Encuentre:

a. f(a)

b. f(a+1)

c. f (a^2 )

d. f (-2/3)

SOLUCIÓN

Hola!!  (⌐■_■)

Solo reemplazaremos para hallar la función

*

$x =a \rightarrowf(x) = f(a)\\\\f(x) = 2x^{2} - x^{4}\\\\f(a) = 2a^{2} - a^{4}$

*

$x =a+1 \rightarrow f(x) = f(a+1)\\\\f(x) = 2x^{2} - x^{4}\\\\f(a+1) = 2(a+1)^{2} - (a+1)^{4}$

*

$x =a^{2} \rightarrowf(x) = f(a^{2})\\\\f(x) = 2x^{2} - x^{4}\\\\f(a^{2}) = 2(a^{2})^{2} - (a^{2})^{4}$

*

$x =- \frac{2}{3} \rightarrow f(x) = f( -\frac{2}{3}) \\\\f(x) = 2x^{2} - x^{4}\\\\f(-\frac{2}{3}) = 2(-\frac{2}{3})^{2} - (-\frac{2}{3})^{4}\\\\f(-\frac{2}{3}) = \frac{8}{9} -\frac{16}{81} = \frac{56}{81}$