Certainly! Let's find [tex]\( f(3) \)[/tex], [tex]\( f(-2) \)[/tex], and [tex]\( f(0) \)[/tex] for the function given by:
[tex]\[ f(x) = \frac{4}{x} + 3 \][/tex]
### 1. Finding [tex]\( f(3) \)[/tex]:
First, substitute [tex]\( x = 3 \)[/tex] into the function:
[tex]\[ f(3) = \frac{4}{3} + 3 \][/tex]
Next, convert 3 into a fraction with the same denominator as [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ 3 = \frac{9}{3} \][/tex]
Now, add the two fractions:
[tex]\[ f(3) = \frac{4}{3} + \frac{9}{3} = \frac{4 + 9}{3} = \frac{13}{3} \][/tex]
So, [tex]\( f(3) = \frac{13}{3} \)[/tex].
### 2. Finding [tex]\( f(-2) \)[/tex]:
Next, substitute [tex]\( x = -2 \)[/tex] into the function:
[tex]\[ f(-2) = \frac{4}{-2} + 3 \][/tex]
Simplify the fraction:
[tex]\[ \frac{4}{-2} = -2 \][/tex]
Then, add 3:
[tex]\[ f(-2) = -2 + 3 = 1 \][/tex]
So, [tex]\( f(-2) = 1 \)[/tex].
### 3. Finding [tex]\( f(0) \)[/tex]:
Finally, substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ f(0) = \frac{4}{0} + 3 \][/tex]
However, division by zero is undefined in mathematics. Therefore, the function [tex]\( f(x) \)[/tex] is not defined at [tex]\( x = 0 \)[/tex]. This means that [tex]\( f(0) \)[/tex] does not exist.
In summary:
- [tex]\( f(3) = \frac{13}{3} \)[/tex]
- [tex]\( f(-2) = 1 \)[/tex]
- [tex]\( f(0) \)[/tex] is undefined because division by zero is not permissible.
