Question

5. Determinaţi funcţia g: R→ R, g(x) = 3x+b, dacă: a) g(1)=3; b) g(2)=-1; c) g(-2) = -2; d) g(3)=0; e) g(4)=0; f) g(0)-1. ​

Answer 1

$g(x) = 3x + b$

a)

$g(1) = 3 \Leftrightarrow 3 \cdot 1 + b = 3 \Leftrightarrow 3 + b = 3 \Leftrightarrow b = 3 - 3 \Leftrightarrow b = 0$

$\implies g(x) = 3x$

b)

$g(2) = -1 \Leftrightarrow 3 \cdot 2 + b = -1 \Leftrightarrow 6 + b = -1 \Leftrightarrow b = - 1 - 6 \Leftrightarrow b = -7$

$\implies g(x) = 3x - 7$

c)

$g(-2) = -2 \Leftrightarrow 3 \cdot (-2) + b = -2 \Leftrightarrow -6 + b = -2 \Leftrightarrow b = -2 + 6 \Leftrightarrow b = 4$

$\implies g(x) = 3x + 4$

d)

$g(3) = 0 \Leftrightarrow 3 \cdot 3 + b = 0 \Leftrightarrow 9 + b = 0 \Leftrightarrow b = -9$

$\implies g(x) = 3x - 9$

e)

$g(4) = 0 \Leftrightarrow 3 \cdot 4 + b = 0 \Leftrightarrow 12 + b = 0 \Leftrightarrow b = -12$

$\implies g(x) = 3x - 12$

f)

$g(0) = 1 \Leftrightarrow 3 \cdot 0 + b = 1 \Leftrightarrow 0 + b = 1 \Leftrightarrow b = 1$

$\implies g(x) = 3x + 1$