Property 6
\(f:\mathbb R\to\mathbb R\)
\(f(-x)=f(x)\qquad x\in\mathbb R\)
function "f" is called even function.
\(f(x)=|x|\)
\(f(x)=\cos x\)
\(f(x)=k\cdot x^{2n}\qquad n\in\mathbb N\quad k\in\mathbb R\)
\(f(x)=k\)
Even functions are symmetrical according to "y" axis.
Functions that are made of even powers of "x" are even functions.
\(f(x)=x^2\)
\(f(x)=3x^4+7\)
\(f(x)=x^6-5x^4+x^2-10\)
→ f(x) even function
\(f(x):\mathbb R\to\mathbb R\)
1.
\(m\in\mathbb R\)
\(f(x)=x^2+mx-6\)
\(\Rightarrow m=?\)
2.
\(a,b,c\in\mathbb R\)
\(f(x)=ax^7+(b+1)x^5+(c-7)x^3+4\)
\(\Rightarrow a+b+c=?\)
3.
\(f(x)=x^2+4-f(-x)\)
\(\Rightarrow f(2)=?\)
4.
\(3f(x)=f(-x)+4x^4-2x^2\)
\(\Rightarrow f(2)=?\)
5.
\(a\in\mathbb R\)
\(f(x)=(a-2)x^3+ax^2+4a\)
\(\Rightarrow f(1)=?\)
6.
\(f(x)=\cos x+|x|+x^4\)
\(\Rightarrow \samefrac{f(-x)}{f(x)}=?\)