Question

given ( f(x)=12x - 4 ) and ( g(x)=x^{2}+7 ), find the following:
( g(-2)=)
( x ) when ( f(x)=17 ) this means ( x=)
( f(x)-g(x)=)

Explanation:

Step1: Calcular \( g(-2) \)

Sustituir \( x = -2 \) en \( g(x)=x^{2}+7 \).
$$g(-2)=(-2)^{2}+7$$
$$g(-2)=4 + 7$$

Step2: Encontrar \( x \) cuando \( f(x)=17 \)

Dado \( f(x)=12x - 4 \), igualar a 17: \( 12x-4 = 17 \).
Sumar 4 a ambos lados: \( 12x=17 + 4=21 \).
Dividir por 12: \( x=\frac{21}{12}=\frac{7}{4}=1.75 \).

Step3: Calcular \( f(x)-g(x) \)

Sustituir \( f(x)=12x - 4 \) y \( g(x)=x^{2}+7 \).
\( f(x)-g(x)=(12x - 4)-(x^{2}+7) \).
Simplificar: \( f(x)-g(x)=12x-4 - x^{2}-7=-x^{2}+12x-11 \).

Answer:

\( g(-2)=11 \)
\( x = 1.75 \)
\( f(x)-g(x)=-x^{2}+12x - 11 \)