Question

Help needed math 3 - 10 points read closely

Answer 1

Hello!

The answer is:

The answer is the fourth option,

$f(-3)=-\frac{1}{3}$

Why?

Piecewise functions are functions that are composed by two or more expressions, the expression to use will depend of the domain or input that we need to evaluate.

We are given the piecewise function:

$\left \{ {{\frac{1}{x}, if x$

There, we know that:

We should use the first expression if the value to evaluate is less than -2.

So, for this case, the function will be:

$f(x)=\frac{1}{x}$

We should use the second expression if the value to evaluate is greater or equal than 2.

So, for this case, the function will be:

$f(x)=x^{2}$

Now, since we are given that the value to evaluate is -3, and its less than -2, we need to use the first expression, and evaluate it.

$-3$

So, evaluating the function we have:

$f(x)=\frac{1}{x}$

$f(-3)=\frac{1}{-3}$

$f(-3)=-\frac{1}{3}$

Hence, we have that the answer is the fourth option,

$f(-3)=-\frac{1}{3}$

Have a nice day!