Question

Find the value of $f\left(x^2\right),{\left(f\left(x\right)\right)}^2$for the function $f\left(x\right)=x+4$.

Short answer

The value of $f\left(x^2\right)=x^2+4\text{and}{\left(f\left(x\right)\right)}^2=x^2+8x+16$.

Step-by-step solution

Step 1. Evaluate fx2 for the given function.

From the given function,

$f\left(x\right)=x+4....\left(1\right)$

Evaluate $f\left(x^2\right)$gives,

localid="1644526863619" role="math" $$\begin{gathered} f\left(x^2\right)=\left(x^2\right)+4....\left(\text{Substitute}x=x^2\text{in}\left(1\right)\right) \\ =x^2+4 \end{gathered}$$

Step 2. Similarly evaluate fx2 for the given function.

Similarly, evaluate ${\left(f\left(x\right)\right)}^2$gives

localid="1644526923512" role="math" $$\begin{gathered} {\left(f\left(x\right)\right)}^2={\left(x+4\right)}^2\mathrm{....}\left(\text{Squared}\left(1\right)\right) \\ =x^2+8x+16 \end{gathered}$$

Step 3. Description of steps.

From the obtained values $f\left(x^2\right)=x^2+4\text{and}{\left(f\left(x\right)\right)}^2=x^2+8x+16$.