Question

given the functions $f(x)=x^2 + 4$ and $h(x)=x - 2$, find $(f - h)(-4)$
26
6
12
14

Explanation:

Step1: Define \((f - h)(x)\)

The difference of two functions \(f(x)\) and \(h(x)\) is defined as \((f - h)(x)=f(x)-h(x)\). Given \(f(x)=x^{2}+4\) and \(h(x)=x - 2\), we substitute these into the formula:
\((f - h)(x)=(x^{2}+4)-(x - 2)\)
Simplify the right - hand side:
\((f - h)(x)=x^{2}+4 - x + 2=x^{2}-x + 6\)

Step2: Evaluate \((f - h)(-4)\)

Substitute \(x=-4\) into the function \((f - h)(x)=x^{2}-x + 6\).
First, calculate \(x^{2}\) when \(x = - 4\): \((-4)^{2}=16\)
Then, calculate \(-x\) when \(x=-4\): \(-(-4)=4\)
Now, substitute these values into the function:
\((f - h)(-4)=(-4)^{2}-(-4)+6\)
\(=16 + 4+6\)
\(=26\)

Answer:

26