SOLUTION: Suppose f(x)=(x-5)2 and g(x)=√x+7. Evaluate the following expressions. A)f(g(5)) B)g(f(−13))

Algebra ->  Finance -> SOLUTION: Suppose f(x)=(x-5)2 and g(x)=√x+7. Evaluate the following expressions. A)f(g(5)) B)g(f(−13))      Log On


   

Question 1127364: Suppose f(x)=(x-5)2 and g(x)=√x+7. Evaluate the following expressions.
A)f(g(5))
B)g(f(−13))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Suppose f%28x%29=%28x-5%29%5E2 and g%28x%29=sqrt%28x%2B7%29.
Evaluate the following expressions.
A)
f%28g%285%29%29
first find
f%28g%28x%29%29=%28sqrt%28x%2B7%29%29


f%28g%28x%29%29=x%2B7-10sqrt%28x%2B7%29%2B25
f%28g%28x%29%29=x%2B37+-10sqrt%2812%29
if x=5, we have
f%28g%285%29%29=37+-10sqrt%2812%29
f%28g%285%29%29=37+-10%2A3.46
f%28g%285%29%29=37+-34.6
f%28g%285%29%29=2.4

B)
g%28f%28-13%29%29
g%28f%28x%29%29+=g%28%28x-5%29%5E2%29
g%28f%28x%29%29=sqrt%28%28x-5%29%5E2%2B7%29
g%28f%28x%29%29=sqrt%28x%5E2-10x%2B25%2B7%29
g%28f%28x%29%29=sqrt%28x%5E2-10x%2B32%29
if x=-13, we have
g%28f%28-13%29%29+=sqrt%28%28-13%29%5E2-10%28-13%29%2B32%29
g%28f%28-13%29%29+=sqrt%28169%2B130%2B32%29
g%28f%28-13%29%29+=18.19