Simplified formula for a function

Question

if f(x)= e^6x      g(x)= 5x+3      h(x)= √x

 

Find a simplified formula for the function below:

 

f(g(x))h(x)

Answer 1

f(g(x)) means plug g(x) in for x in the equation for f(x):

 

f(g(x)) = e^{6 g(x)} = e^{6 (5x+3)} = e ^{30x + 18}

 

You then multiply this by the expression for h(x):

 

e ^{30x + 18} √x

 

or

 

x^1/2 e ^{30x + 18}