Question

f:R-R,f(x)=3x la puterea 4 +2xla puterea2+1 arătați ca f este para​

Answer 1

$f:\mathbb{R}\rightarrow\mathbb{R},f(x)=3 {x}^{4} + 2 {x}^{2} + 1$

$f \: para < = > f( - x) = f(x)$

$3 \times {( - x)}^{4} + 2 \times {( - x)}^{2} + 1 = 3 {x}^{4} + 2 {x}^{2} + 1$

$3 \times {( - 1 \times x)}^{4} + 2 \times {( - 1 \times x)}^{2} + 1 = 3 {x}^{4} + 2 {x}^{2} + 1$

$3 \times {( - 1)}^{4} \times {x}^{4} + 2 \times {( - 1)}^{2} \times {x}^{2} + 1 = 3 {x}^{4} + 2 {x}^{2} + 1$

$3 \times 1 \times {x}^{4} + 2 \times 1 \times {x}^{2} + 1 = 3 {x}^{4} + 2 {x}^{2} + 1$

$3 {x}^{4} + 2 {x}^{2} + 1 = 3 {x}^{4} + 2 {x}^{2} + 1 \: (A)$

$= > f \: para$