Question

In Problems 39– 46, find the following for each function:

$\left(a\right)f\left(0\right)\left(b\right)f\left(1\right)\left(c\right)f(-1)\left(d\right)f(-x)\left(e\right)-f\left(x\right)\left(f\right)f(x+1)\left(g\right)f\left(x\right)\left(h\right)f(x+h)$

$f\left(x\right)=\left|x\right|+4$

Short answer

The value of

$$\begin{gathered} f\left(0\right)=4 \\ f\left(1\right)=5 \\ f(-1)=5 \\ f(-x)=x+4 \\ -f\left(x\right)=-\left|x\right|-4 \\ f(x+1)=x+5 \\ f\left(x\right)=\left|x\right|+4 \\ f(x+h)=x+h+4 \end{gathered}$$

Step-by-step solution

Step 1. Given Information

We have to find the value for each function:

$\left(a\right)f\left(0\right)\left(b\right)f\left(1\right)\left(c\right)f(-1)\left(d\right)f(-x)\left(e\right)-f\left(x\right)\left(f\right)f(x+1)\left(g\right)f\left(x\right)\left(h\right)f(x+h)$

The given equation is$f\left(x\right)=\left|x\right|+4$

Part (a) Step 1. We find the value of  f(0)Putting x=0 in the given question.

$$\begin{gathered} f\left(0\right)=\left|0\right|+4 \\ f\left(0\right)=4 \end{gathered}$$

Part (b) Step 1. We find the value of  f(1)Putting x=1 in the given question.

$$\begin{gathered} f\left(1\right)=\left|1\right|+4 \\ f\left(1\right)=1+4 \\ f\left(1\right)=5 \end{gathered}$$

Part (c) Step 1. We find the value of f(-1)Putting x=-1 in the given question.

$$\begin{gathered} f(-1)=\left|-1\right|+4 \\ f(-1)=1+4 \\ f(-1)=5 \end{gathered}$$

Part (d) Step 1. We find the value of f(-x)Putting x=-x in the given question.

$$\begin{gathered} f(-x)=\left|-x\right|+4 \\ f(-x)=x+4 \end{gathered}$$

Part (e) Step 1. We find the value of -f(x)To find the value we multiply the given equation by -sign

$$\begin{gathered} -f\left(x\right)=-\left(\left|x\right|+4\right) \\ -f\left(x\right)=-\left|x\right|-4 \end{gathered}$$

Part (f) Step 1. We find the value of f(x+1)Putting x=x+1 in the given question.

$$\begin{gathered} f(x+1)=\left|x+1\right|+4 \\ f(x+1)=x+1+4 \\ f(x+1)=x+5 \end{gathered}$$

Part (g) Step 1. We find the value of f(x)

The value of$f\left(x\right)=\left|x\right|+4$

Part (h) Step 1. We find the value of f(x+h)Putting x=x+h in the given question.

$$\begin{gathered} f(x+h)=\left|x+h\right|+4 \\ f(x+h)=x+h+4 \end{gathered}$$