Questions: Find the following for the function f(x)=x+10. (a) f(0) (b) f(9) (c) f(-9) (e) -f(x) (d) f(-x) (f) f(x+5) (g) f(3 x) (h) f(x+h) (a) f(0)=10 (b) f(9)=19 (c) f(-9)=

Find the following for the function f(x)=x+10. (a) f(0) (b) f(9) (c) f(-9) (e) -f(x) (d) f(-x) (f) f(x+5) (g) f(3 x) (h) f(x+h) (a) f(0)=10 (b) f(9)=19 (c) f(-9)=
Transcript text: Find the following for the function $f(x)=|x|+10$. (a) $f(0)$ (b) $f(9)$ (c) $f(-9)$ (e) $-f(x)$ (d) $f(-x)$ (f) $f(x+5)$ (g) $f(3 x)$ (h) $f(x+h)$ (a) $f(0)=10$ (b) $f(9)=19$ (c) $f(-9)=$ $\square$
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Solution

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Solution Steps

To solve the given problem, we need to evaluate the function \( f(x) = |x| + 10 \) for specific values of \( x \). The function involves the absolute value of \( x \), which means it will always return a non-negative value. We will substitute the given values into the function and compute the results.

Solution Approach
  1. For \( f(0) \), substitute \( x = 0 \) into the function.
  2. For \( f(9) \), substitute \( x = 9 \) into the function.
  3. For \( f(-9) \), substitute \( x = -9 \) into the function.
Step 1: Evaluate \( f(0) \)

To find \( f(0) \), substitute \( x = 0 \) into the function \( f(x) = |x| + 10 \).

\[ f(0) = |0| + 10 = 0 + 10 = 10 \]

Step 2: Evaluate \( f(9) \)

To find \( f(9) \), substitute \( x = 9 \) into the function.

\[ f(9) = |9| + 10 = 9 + 10 = 19 \]

Step 3: Evaluate \( f(-9) \)

To find \( f(-9) \), substitute \( x = -9 \) into the function.

\[ f(-9) = |-9| + 10 = 9 + 10 = 19 \]

Final Answer

  • \( f(0) = \boxed{10} \)
  • \( f(9) = \boxed{19} \)
  • \( f(-9) = \boxed{19} \)
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