Question

Em quais dos itens há uma lei de formação de função exponencial? Justifique sua resposta. ​

Answer 1

Explicação passo-a-passo:

Uma função exponencial é da forma $\sf f(x)=a^x$, sendo $\sf a > 0~e~a \ne 1$

Logo, são funções exponenciais:

a) $\sf f(x)=2^{x+1}$

c) $\sf f(x)=\Big(\dfrac{1}{4}\Big)^{2x}$

d) $\sf f(x)=2^{\frac{x}{2}}$

e) $\sf f(x)=-2^{2x}$

=> a), c), d), e)

15)

a)

$\sf f(x)=\Big(\dfrac{1}{2}\Big)^x$

$\sf f(0)=\Big(\dfrac{1}{2}\Big)^0$

$\sf \red{f(0)=1}$

b)

$\sf f(x)=\Big(\dfrac{1}{2}\Big)^x$

$\sf f(4)=\Big(\dfrac{1}{2}\Big)^4$

$\sf f(4)=\dfrac{1^4}{2^4}$

$\sf \red{f(4)=\dfrac{1}{16}}$

c)

$\sf f(x)=\Big(\dfrac{1}{2}\Big)^x$

$\sf f(1)=\Big(\dfrac{1}{2}\Big)^1$

$\sf \red{f(1)=\dfrac{1}{2}}$

d)

$\sf f(x)=\Big(\dfrac{1}{2}\Big)^x$

$\sf f(2)=\Big(\dfrac{1}{2}\Big)^2$

$\sf f(2)=\dfrac{1^2}{2^2}$

$\sf \red{f(4)=\dfrac{1}{4}}$

e)

$\sf f(x)=\Big(\dfrac{1}{2}\Big)^x$

$\sf f\Big(\dfrac{1}{4}\Big)=\Big(\dfrac{1}{2}\Big)^{\frac{1}{4}}$

Lembre-se que $\sf a^{\frac{b}{c}}=\sqrt[c]{a^b}$

Assim:

$\sf f\Big(\dfrac{1}{4}\Big)=\Big(\dfrac{1}{2}\Big)^{\frac{1}{4}}$

$\sf f\Big(\dfrac{1}{4}\Big)=\sqrt[4]{\Big(\dfrac{1}{2}\Big)^1}$

$\sf f\Big(\dfrac{1}{4}\Big)=\sqrt[4]{\dfrac{1}{2}}$

$\sf f\Big(\dfrac{1}{4}\Big)=\dfrac{1}{\sqrt[4]{2}}$

$\sf f\Big(\dfrac{1}{4}\Big)=\dfrac{1}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^3}}$

$\sf f\Big(\dfrac{1}{4}\Big)=\dfrac{\sqrt[4]{2^3}}{\sqrt[4]{2^4}}$

$\sf \red{f\Big(\dfrac{1}{4}\Big)=\dfrac{\sqrt[4]{8}}{2}}$