Question

determine o dominio e a imagem das funções

Answer 1

$\large\boxed{\begin{array}{l}\tt a)~\sf f(x)=\dfrac{8x}{x\cdot(4x-5)\cdot(2x+1)}\\\sf devemos~garantir~que~o~denominador~n\tilde ao~se~anule.\\\sf x\ne0\\\sf 4x-5\ne0\\\sf 4x\ne5\\\sf x\ne\dfrac{5}{4}\\\sf 2x+1\ne0\\\sf 2x\ne-1\\\sf x\ne-\dfrac{1}{2}\\\sf Dom~f(x)=\bigg\{x\in\mathbb{R}/x\ne0,x\ne\dfrac{5}{4},x\ne-\dfrac{1}{2}\bigg\}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~logaritmo}\\\sf \ell o_ba=x\Longleftrightarrow b^x=a\begin{cases}\sf a>0\\\sf b<0\\\sf b\ne1\end{cases}\\\tt b)~\sf g(x)=\ell n(25-2x)\\\sf 25-2x>0\\\sf -2x>-25\cdot(-1)\\\sf 2x<25\\\sf x<\dfrac{25}{2}\\\sf Dom~g(x)=\bigg\{x\in\mathbb{R}/x<\dfrac{25}{2}\bigg\}\end{array}}$