Question

21
a function is shown.
$f(x)=2x^2 + 3x + 4$
the function $g(x)$ is given by $g(x)=3cdot f(x)+1$.

• what is $g(x)$ in terms of $x$? enter your answer on the first answer line.
• what is the value of $g(0)$? enter your answer on the second answer line.

Explanation:

First Sub - Question: Find \(g(x)\) in terms of \(x\)

Step 1: Substitute \(f(x)\) into \(g(x)\)

We know that \(f(x)=2x^{2}+3x + 4\) and \(g(x)=3\cdot f(x)+1\). Substitute \(f(x)\) into the formula for \(g(x)\):
\(g(x)=3(2x^{2}+3x + 4)+1\)

Step 2: Distribute the 3

Using the distributive property \(a(b + c + d)=ab+ac + ad\), we get:
\(g(x)=3\times2x^{2}+3\times3x+3\times4 + 1=6x^{2}+9x + 12 + 1\)

Step 3: Combine like terms

Combine the constant terms \(12\) and \(1\):
\(g(x)=6x^{2}+9x+13\)

Step 1: Substitute \(x = 0\) into \(g(x)\)

We have \(g(x)=6x^{2}+9x + 13\). Substitute \(x = 0\) into this function:
\(g(0)=6\times(0)^{2}+9\times(0)+13\)

Step 2: Simplify the expression

Since \(6\times(0)^{2}=0\) and \(9\times(0)=0\), we have:
\(g(0)=0 + 0+13=13\)

Answer:

\(6x^{2}+9x + 13\)

Second Sub - Question: Find \(g(0)\)