Question

Evaluate the function f(r) the square root of r+6 -4 at the given values of the independent variable and simplify. a. f(-6) b. f(43) c. f(x-6)

Answer 1

Write out the function given

`f(r)=\sqrt[]{r+6}-4`

The independent variable in the function above is r.

Hence

For f(-6), we have r=-6,

substitute into the function given

`\begin{gathered} f(-6),\text{ r=-6} \\ f(-6)=\sqrt[]{-6+6}-4 \\ f(-6)=\sqrt[]{0}-4=4 \\ Then,f(-6)=-4 \end{gathered}`

Hence, F(-6) = - 4

For f(43), we have

`\begin{gathered} f(43),\text{ r=43} \\ \text{Then} \\ f(43)=\sqrt[]{43+6}-4 \\ f(43)=\sqrt[]{49}-4=7-4=3 \\ \text{Hence, f(43) = 3} \end{gathered}`

Thus, F(43) = 3

For f(x - 6), we have

`\begin{gathered} f(x-6)\Rightarrow r=x-6 \\ \text{Then } \\ f(x-6)=\sqrt[]{x-6+6}-4 \\ f(x-6)=\sqrt[]{x}-4 \end{gathered}`

Thus, f(x-6) = (√x) - 4