Questions: Evaluate the function f(r)=sqrt(r+3)+9 at the given values of the independent variable and simplify. a. f(-3) b. f(61) c. f(x-3)

Solution Steps

To evaluate the function \( f(r) = \sqrt{r+3} + 9 \) at the given values of the independent variable, we will substitute the values into the function and simplify the result.

a. For \( f(-3) \), substitute \( r = -3 \) into the function. b. For \( f(61) \), substitute \( r = 61 \) into the function. c. For \( f(x-3) \), substitute \( r = x-3 \) into the function.

To evaluate \( f(-3) \), substitute \( r = -3 \) into the function \( f(r) = \sqrt{r+3} + 9 \): \[ f(-3) = \sqrt{-3 + 3} + 9 = \sqrt{0} + 9 = 0 + 9 = 9 \]

To evaluate \( f(61) \), substitute \( r = 61 \) into the function \( f(r) = \sqrt{r+3} + 9 \): \[ f(61) = \sqrt{61 + 3} + 9 = \sqrt{64} + 9 = 8 + 9 = 17 \]

To evaluate \( f(x-3) \), substitute \( r = x-3 \) into the function \( f(r) = \sqrt{r+3} + 9 \): \[ f(x-3) = \sqrt{(x-3) + 3} + 9 = \sqrt{x} + 9 \] For \( x = 5 \): \[ f(5-3) = \sqrt{5} + 9 \approx 2.2361 + 9 = 11.2361 \]

Final Answer