Question

E3 urgent pls!!!!!!!!!!!!!!!!!!!​

Answer 1

$f:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,f(x)=3x+7$

$(g \circ f)(x) = - 6x - 5 \: \: \: ,\forall\:x \: \in \: \mathbb{R}$

$(g \circ f)(x) = g(f(x)) = g(3x + 7)$

$Fie \: g:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,g(x)=ax+b$

$g(3x + 7) = a(3x + 7) + b$

$g(3x + 7) = 3ax + 7a + b$

$3ax + 7a + b = - 6x - 5$

$3a = - 6 \: | \div 3$

$a = - 2$

$7a + b = - 5$

$7 \times ( - 2) + b = - 5$

$- 14 + b = - 5$

$b = - 5 + 14$

$b = 9$

$= > g(x) = - 2x + 9$