22) $g(x)=2x + 3$ $h(x)=x^{2}-3$ find $2g(x)-2h(x)$

Explanation:

Step1: Substitute the functions

Substitute $g(x)=2x + 3$ and $h(x)=x^{2}-3$ into $2g(x)-2h(x)$. $2(2x + 3)-2(x^{2}-3)$

Step2: Distribute the coefficients

Use the distributive property $a(b + c)=ab+ac$. $2\times2x+2\times3-2\times x^{2}+2\times3$ $4x + 6-2x^{2}+6$

Step3: Combine like - terms

Combine the constant terms. $-2x^{2}+4x+(6 + 6)$ $-2x^{2}+4x + 12$

Answer:

$-2x^{2}+4x + 12$