Question

Para qual subconjunto do domínio de f(x)= (0, 6)^2x+1 temos 27/125<f(x)=≤1?
a) [-1/2, 1[
b)[-1/2, 1]
c)]-1/2, 1]
d)]-1/2, 1[
​

Answer 1

Explicação passo-a-passo:

• $\sf (0,6)^{2x+1}=\dfrac{27}{125}$

$\sf \left(\dfrac{3}{5}\right)^{2x+1}=\left(\dfrac{3}{5}\right)^3$

Igualando os expoentes:

$\sf 2x+1=3$

$\sf 2x=3-1$

$\sf 2x=2$

$\sf x=\dfrac{2}{2}$

$\sf \green{x=1}$

• $\sf (0,6)^{2x+1}=1$

$\sf \left(\dfrac{3}{5}\right)^{2x+1}=\left(\dfrac{3}{5}\right)^0$

Igualando os expoentes:

$\sf 2x+1=0$

$\sf 2x=-1$

$\sf \green{x=\dfrac{-1}{2}}$

Logo, $\sf \red{D(f)=\left[~\dfrac{-1}{2},1~\right[}$

Letra A