### Home > APCALC > Chapter 1 > Lesson 1.2.2 > Problem1-38

1-38.

If $f(x)=\frac{3}{x^2}+1$ .

1. State the domain and range of $f$.

Domain: Notice the $x$ in the denominator. What values of $x$ must be excluded?
Range: Notice that $x$ is squared. What does this mean about the outputs of $f(x)$? Furthermore, what will the $+1$ do to the range?

2. Write expressions for $f(−x)$, $f(\sqrt { x })$, and $f(x + h)$.

$f(x)=\frac{3}{x^{2}}+1$

$f(-x)=\frac{3}{-x^{2}}+1=\ \ \ \ \ \ \text{SIMPLIFY}$

$f(\sqrt{x})=\frac{3}{(\sqrt{x})^{2}}+1=\ \ \ \ \ \ \text{ SIMPLIFY}$

$f(x+h)=\frac{3}{(x+h)^{2}}+1=\ \ \ \ \ \text{SIMPLIFY}$

Use the eTool below to view the graphs.
Click the link at right for the full version of the eTool: Calc 1-38 HW eTool