Question

Sendo f(x) =3x-1 /x²+1
A) f(-1)+f(-2)=

Answer 1

Dada a função:

$\mathsf{f\left(x\right)=\dfrac{3x-1}{x^2+1}}$

= = = = =

O valor da função quando $\mathsf{x=-1}$:

$\mathsf{f\left(-1\right)=\dfrac{\left[3\cdot \left(-1\right)\right]-1}{\left(-1\right)^2+1}}\\\\\\\mathsf{f\left(-1\right)=\dfrac{-3-1}{1+1}}\\\\\\\mathsf{f\left(-1\right)=\dfrac{-4}{2}}\\\\\\\boxed{\mathsf{f\left(-1\right)=-2}}$

= = = = =

O valor da função quando $\mathsf{x=-2}$:

$\mathsf{f\left(-2\right)=\dfrac{\left[3\cdot \left(-2\right)\right]-1}{\left(-2\right)^2+1}}\\\\\\\mathsf{f\left(-2\right)=\dfrac{-6-1}{4+1}}\\\\\\\boxed{\mathsf{f\left(-2\right)=-\dfrac{7}{5}}}$

= = = = =

Logo:

$\mathsf{=f\left(-1\right)+f\left(-2\right)}\\\\\\\mathsf{=-2-\dfrac{7}{5}}\\\\\\\mathsf{=-\dfrac{5\cdot 2}{5}-\dfrac{7}{5}}\\\\\\\mathsf{=-\dfrac{10}{5}-\dfrac{7}{5}}\\\\\\\mathsf{=-\dfrac{10-7}{5}}\\\\\\\boxed{\mathsf{-\dfrac{3}{5}\:\:\:ou\:\:\:-0,12}}\: \:\ \checkmark$