Question 1127364

 Suppose {{{f(x)=(x-5)^2}}} and {{{g(x)=sqrt(x+7)}}}. 

Evaluate the following expressions.
A)

{{{f(g(5))}}}

first find

{{{f(g(x))=(sqrt(x+7))}}}
 
{{{f(g(x))=(sqrt(x+7)-5)^2

{{{f(g(x))= (sqrt(x+7))^2-2*5sqrt(x+7)+25}}}

{{{f(g(x))=x+7-10sqrt(x+7)+25}}}

{{{f(g(x))=x+37 -10sqrt(12)}}}

if {{{x=5}}}, we have

{{{f(g(5))=37 -10sqrt(12)}}}

{{{f(g(5))=37 -10*3.46}}}

{{{f(g(5))=37 -34.6}}}

{{{f(g(5))=2.4}}}


B)

{{{g(f(-13))}}}

{{{g(f(x)) =g((x-5)^2)}}}

{{{g(f(x))=sqrt((x-5)^2+7)}}}

{{{g(f(x))=sqrt(x^2-10x+25+7)}}}

{{{g(f(x))=sqrt(x^2-10x+32)}}}

if {{{x=-13}}}, we have

{{{g(f(-13)) =sqrt((-13)^2-10(-13)+32)}}}

{{{g(f(-13)) =sqrt(169+130+32)}}}

{{{g(f(-13)) =18.19}}}