Question

Suppose that the function f is defined, for all real numbers, as follows.1--x' +4 if x13f(x) = 24if x=1Find f(-4).f(1), and f(3).1(-4) = 0음f(1) = 0X Х?f(3) =

Answer 1

`\begin{gathered} f(-4)=-(4)/(3) \\ f(1)=4 \\ f(3)=1 \end{gathered}`

Explanation:

These types of functions are called Piecewise-defined functions since it use a different formula for different parts of its domain because it has a point of discontinuity.

We have the following function:

`f(x)=\begin{cases}-(1)/(3)x^2+4\rightarrow ifx\\e1^{} \\ \text{ 4 if x=1}\end{cases}`

So, to find f(-4), we need to substitute x=-4 into the function for x≠1.

`\begin{gathered} f(-4)=(-1)/(3)(-4)^2+4 \\ f(-4)=-(1)/(3)(16)+4 \\ f(-4)=-(16)/(3)+4 \\ f(-4)=-(4)/(3) \end{gathered}`

Now, for f(1) we know that the outcome is 4.

`f(1)=4`

Then, for f(3), substitute x=3 into the function for x≠1.

`\begin{gathered} f(3)=-(1)/(3)(3)^2+4 \\ f(3)=-(1)/(3)(9)+4 \\ f(3)=1 \end{gathered}`