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Math  /  Algebra

QuestionEvaluate the function f(r)=r+3+9f(r)=\sqrt{r+3}+9 at the given values of the independent variable and simplify. a. f(−3)f(-3) b. f(97)\mathrm{f}(97) c. f(x−3)f(x-3) a. f(−3)=f(-3)= □\square (Simplify your answer.)

Studdy Solution

STEP 1

1. The function f(r)=r+3+9 f(r) = \sqrt{r+3} + 9 is defined for values of r r such that r+3≥0 r + 3 \geq 0 .
2. We are evaluating the function at specific values of r r and simplifying the results.

STEP 2

1. Evaluate the function at r=−3 r = -3 .
2. Evaluate the function at r=97 r = 97 .
3. Evaluate the function at r=x−3 r = x - 3 .

STEP 3

Evaluate f(−3) f(-3) :
f(−3)=−3+3+9 f(-3) = \sqrt{-3 + 3} + 9 f(−3)=0+9 f(-3) = \sqrt{0} + 9 f(−3)=0+9 f(-3) = 0 + 9 f(−3)=9 f(-3) = 9
The simplified answer for f(−3) f(-3) is 9 \boxed{9} .

STEP 4

Evaluate f(97) f(97) :
f(97)=97+3+9 f(97) = \sqrt{97 + 3} + 9 f(97)=100+9 f(97) = \sqrt{100} + 9 f(97)=10+9 f(97) = 10 + 9 f(97)=19 f(97) = 19
The simplified answer for f(97) f(97) is 19 \boxed{19} .

STEP 5

Evaluate f(x−3) f(x-3) :
f(x−3)=(x−3)+3+9 f(x-3) = \sqrt{(x-3) + 3} + 9 f(x−3)=x+9 f(x-3) = \sqrt{x} + 9
The simplified expression for f(x−3) f(x-3) is x+9 \boxed{\sqrt{x} + 9} .

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