Question

(Fuvest-SP) Seja f(x) = 2^2x+1 se a e b são tais que f(a)= 4f(b), pode-se afirmar que :
a) a+b=2
b) a+b=1
c) a-b=3
d) a-b=2
e) a-b=1

Answer 1

$f(x) = 2^{2x +1} ~~~~~~~~f(a) = 4f(b)$

$2^{2a +1} = 4.2^{2b+1}$
$2^{2a +1} = 2^2.2^{2b+1}$
$\not2^{2a +1} = \not2^{2b+1+ 2}$
$2a+1= 2b+ 3$
$2a-2b = 3-1$
$2(a-b) = 2$
$a-b = \frac{2}{2}$
$a-b = 1$

$\boxed{alternativa~~ e)}$