Question

Seja f(x) uma função real, tal que f(1)= 1 e f(x+1)=2f(x) +1. O valor do f(6) é?​

Answer 1

$\text{f(6})} = \ ? \\\\ \text {f(1)} = 1 \\\\ \text{f(x+1)} = 2.\text{f(x)}+1$

Façamos :

$\text x = 1 \to \text{f(1+1)}=2.\text{f(1)}+1 \to 2.1+1 \to \text{f(2)}=3 \\\\ \text x= 2 \to \text{f(2+1)}=2.\text{f(2)}+1 \to 2.3+1 \to \text {f(3)} = 7 \\\\ \text x=3 \to \text{f(3+1)} = 2.\text{f(3)}+1 \to 2.7+1 \to \text {f(4)} = 15 \\\\ \text x = 4 \to \text{f(4+1)}=2.\text{f(4)}+1 \to 2.15+1\to \text{f(5)} = 31 \\\\ \text x = 5 \to \text{f(5+1)}=2.\text{f(5)}+1 \to 2.31+1 \to \text{f(6)}=63 \\\\ \underline{\text{portanto}}: \\\\\ \huge\boxed{\text{f(6)}=63}\checkmark$