SOLUTION: Evaluate h(2), where h=gºf. f(x)= 1/2x+1, g(x)=sqrt(x)

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Question 1125128: Evaluate h(2), where h=gºf.
f(x)= 1/2x+1, g(x)=sqrt(x)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I came to fix the errors in the post of the other tutor.


You may go in  any  of two ways.


The first way. 

First evaluate f(2),   where f(x) = %281%2F2%29%2Ax%2B1 :


    f(2) = %281%2F2%29%2A2%2B1 = 1 + 1 = 2.


And then evaluate g(f(2)) = g(2) = sqrt%282%29.


It is your ANSWER.


The second way. 

Start developing the general formula for  gof(x) :


    gof(x) = g(f(x)) = sqrt%28%281%2F2%29x%2B1%29 = sqrt%28%28x%2B2%29%2F2%29


and then substitute x= 2 into this formula


    gof(2) = sqrt%28%282%2B2%29%2F2%29 = sqrt%284%2F2%29 = sqrt%282%29.

By doing any way,  you get the same  ANSWER :   gof(2) = sqrt%282%29.