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Math  /  Algebra

QuestionGiven the function f(x)={x2−9x−3x≠39x=3f(x) = \begin{cases} \frac{x^2 - 9}{x - 3} & x \neq 3 \\ 9 & x = 3 \end{cases} Calculate the following values: f(2)=f(2) = f(0)=f(0) = f(3)=f(3) =

Studdy Solution

STEP 1

What is this asking? We're given a *piecewise function* f(x)f(x) and we need to find its value at x=2x = 2, x=0x = 0, and x=3x = 3. Watch out! Piecewise functions can be tricky!
Make sure to plug in the xx value into the *correct* piece of the function.

STEP 2

1. Evaluate f(2)f(2)
2. Evaluate f(0)f(0)
3. Evaluate f(3)f(3)

STEP 3

Since 2≠32 \neq 3, we use the first piece of the function: f(x)=x2−9x−3f(x) = \frac{x^2 - 9}{x - 3}.
Let's **plug in** x=2x = 2. f(2)=22−92−3 f(2) = \frac{2^2 - 9}{2 - 3}

STEP 4

Now, let's **simplify** the numerator and denominator: f(2)=4−92−3=−5−1 f(2) = \frac{4 - 9}{2 - 3} = \frac{-5}{-1}

STEP 5

Dividing −5-5 by −1-1 gives us our **result**: f(2)=5 f(2) = 5

STEP 6

Since 0≠30 \neq 3, we again use the first piece: f(x)=x2−9x−3f(x) = \frac{x^2 - 9}{x - 3}. **Substitute** x=0x = 0. f(0)=02−90−3 f(0) = \frac{0^2 - 9}{0 - 3}

STEP 7

**Simplify** the numerator and denominator: f(0)=−9−3 f(0) = \frac{-9}{-3}

STEP 8

Dividing −9-9 by −3-3 gives us: f(0)=3 f(0) = 3

STEP 9

Now, x=3x = 3, so we use the *second* piece of the function: f(x)=9f(x) = 9.
This one is super straightforward! f(3)=9 f(3) = 9

STEP 10

f(2)=5f(2) = 5 f(0)=3f(0) = 3 f(3)=9f(3) = 9

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