evaluate the function ( f(r)=sqrt{r + 8}+5 ) at the given values of the independent variable and…

evaluate the function ( f(r)=sqrt{r + 8}+5 ) at the given values of the independent variable and simplify.\na. ( f(-8) ) b. ( f(56) ) c. ( f(x - 8) )\na. ( f(-8)=5 ) (simplify your answer.)\nb. ( f(56)=13 ) (simplify your answer.)\nc. ( f(x - 8)=square ) (simplify your answer.)

evaluate the function ( f(r)=sqrt{r + 8}+5 ) at the given values of the independent variable and simplify.\na. ( f(-8) ) b. ( f(56) ) c. ( f(x - 8) )\na. ( f(-8)=5 ) (simplify your answer.)\nb. ( f(56)=13 ) (simplify your answer.)\nc. ( f(x - 8)=square ) (simplify your answer.)

Answer

Explanation:

Step1: Substitute (r = x - 8) into the function

Given (f(r)=\sqrt{r + 8}+5), when (r=x - 8), we have (f(x - 8)=\sqrt{(x - 8)+8}+5).

Step2: Simplify the expression inside the square - root

Simplify ((x - 8)+8). Using the additive inverse property (a+( - a)=0), where (a = 8), we get ((x - 8)+8=x+( - 8 + 8)=x+0=x). So (f(x - 8)=\sqrt{x}+5).

Answer:

(f(x - 8)=\sqrt{x}+5)