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)

Transcript text: 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

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.

Step 1: Evaluate $ f(-3) $

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

Step 2: Evaluate $ f(61) $

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

Step 3: Evaluate $ f(x-3) $

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 $: \[ f(5-3) = \sqrt{5} + 9 \approx 2.2361 + 9 = 11.2361 \]