SOLUTION: <pre><b>if f(x)=3x+1,and g(x)=(x²+5x)^-1/2,find g(f(x)) </pre>

if f(x)=3x+1,and g(x)=(x2+5x)-1/2,find g(f(x))

g(A) means to plug in A for x in the right side of g(x) and simplify.

So,

g(f(x)) means to plug in f(x) for x in the right side of g(x) and 
simplify.

But since f(x) = 3x+1

g(f(x)) means to plug in 3x+1 for x in the right side of g(x) and 
simplify. 

So we want to take out all the x's in this:

g(x)=(x2 + 5x)-1/2

putting blanks in place of all the x's:

g(____) = (______2 + 5______)-1/2

I will change the parentheses on the right to brackets to avoid
parentheses within parentheses, since parentheses must go in the 
blanks on the right.  The left already has parentheses.

g(____) = [______2 + 5______]-1/2

Now fill in all the blanks where x was with f(x) written as what 
it is given equal to, namely (3x+1) 

So g(f(x)) =

g(3x+1) = [(3x+1)2 + 5(3x+1)]-1/2

g(3x+1) = [(3x+1)2 + 5(3x+1)]-1/2

        = [(3x+1)(3x+1) + 5(3x+1)]-1/2

        = [9x2+6x+1 + 15x+5]-1/2

        = (9x2+21x+6)-1/2

Edwin