SOLUTION
Write out the function given
[tex]f(r)=\sqrt[]{r+6}-4[/tex]
The independent variable in the function above is r.
Hence
For f(-6), we have r=-6,
substitute into the function given
[tex]\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}[/tex]
Hence, F(-6) = - 4
For f(43), we have
[tex]\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}[/tex]
Thus, F(43) = 3
For f(x - 6), we have
[tex]\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}[/tex]
Thus, f(x-6) = (√x) - 4
