Refer to function f,g and h. Evaluate the function for the given value of x. write any number in the answer as an integer or a simplified fraction.

Question

Refer to function f,g and h. Evaluate the function for the given value of x. write any number in the answer as an integer or a simplified fraction.

 

f(x)=x^3+6x

g(x)= under root =3x

h(x)=4x+5

 

(h º f)(5) is 

Answer 1

These are composite functions and are worked from the inside out.

 

The first thing we have to recall is that (f º g) (5) = f(g(5))

Now with f(g(5)), you have to first recognize that x=5. Using that solve for g(5). You would then take that answer and use it as your x for the f(x).

So g(x) = √(3x) = √[(3)(5)] = √(15)

f(x) = x³ + 6x
Solve for f(x) where x = √(15).

f(√(15)) = [√(15)]³ + 6 (√(15))

 

[√(15)]³ = {[√(15)]²}{[√(15)]} = 15 √(15)

 

We have 15 √(15) + 6 √(15) = 25 √(15)

So f(g(5)) = 25 √(15).

I hope this helps.