Question

Find the value of $f\left(x+2\right),f\left(x\right)+f\left(2\right)$for the function $f\left(x\right)=x^2+1$.

Short answer

The value of $f\left(x+2\right)=x^2+4x+5\text{and}$$f\left(x\right)+f\left(2\right)=x^2+6$.

Step-by-step solution

Step 1. Evaluate fx+2 for the function.

From the given function,

$f\left(x\right)=x^2+1....\left(1\right)$

Evaluate the value of function at $x=x+2$gives,

role="math" localid="1644524632787" $$\begin{gathered} f\left(x+2\right)={\left(x+2\right)}^2+1....\left(\text{Substitute}x=x+2\text{in}\left(1\right)\right) \\ =x^2+4x+5 \end{gathered}$$

Step 2. Similarly evaluate fx+f2 for the function.

Similarly, evaluate $f\left(x\right)+f\left(2\right)$for the function (1) gives,

role="math" localid="1644524745913" $$\begin{gathered} f\left(x\right)+f\left(2\right)=\left({\left(x\right)}^2+1\right)+\left({\left(2\right)}^2+1\right) \\ =x^2+1+5 \\ =x^2+6 \end{gathered}$$

Step 3. DESCRIPTION OF STEPS.

From the obtained values $f\left(x+2\right)=x^2+4x+5\text{and}$$f\left(x\right)+f\left(2\right)=x^2+6$.