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question 11
let ( f(x)=x^{2}+3x + 5 ) and ( g(x)=4x + 1 ). which of the following is ( g(f(x)) )?
( 4x^{2}+12x - 11 )
( 16x^{2}+22x + 9 )
( 4x^{2}+10x + 12 )
( 8x^{2}+20x + 9 )
nothing in this list is correct.

Explanation:

Step1: Recall function - composition rule

To find $g(f(x))$, substitute $f(x)$ into $g(x)$. Given $f(x)=x^{2}+3x + 5$ and $g(x)=4x + 1$, we replace $x$ in $g(x)$ with $x^{2}+3x + 5$.

Step2: Perform substitution

$g(f(x))=4(x^{2}+3x + 5)+1$.

Step3: Expand the expression

Using the distributive property $a(b + c + d)=ab+ac + ad$, we have $4(x^{2}+3x + 5)+1=4x^{2}+12x+20 + 1$.

Step4: Simplify the expression

Combine like - terms: $4x^{2}+12x+(20 + 1)=4x^{2}+12x+21$. Since $4x^{2}+12x + 21$ is not in the given list.

Answer:

Nothing in this list is correct.