SOLUTION: I am an old student in College Algebra and I have tried and tried to solve these Compositions of Functions. Your help with the following problems would be greatly appreciated:

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Question 31757: I am an old student in College Algebra and I have tried and tried to solve these Compositions of Functions.
Your help with the following problems would be greatly appreciated:
Find g(f(x))if g(x)=sqrt(2x+3) and f(x)=4x-3.
Find h(f(x)) if h(x)=1/x+2 and f(x)=4x-3
Any thing you can provide would be a great assistance to an old woman.
Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
I am an old student in College Algebra and I have tried and tried to solve these Compositions of Functions.
Your help with the following problems would be greatly appreciated:
Find g(f(x))if g(x)=sqrt(2x+3) and f(x)=4x-3.
Find h(f(x)) if h(x)=1/x+2 and f(x)=4x-3
Any thing you can provide would be a great assistance to an old woman.
THE EASY WAY TO DO THESE PROBLEMS IS AS FOLLOWS
Find g(f(x))if g(x)=sqrt(2x+3) and f(x)=4x-3.
YOU KNOW THAT GIVEN F(X),TO FIND F(2)..OR F(A)..OR.....F(TANIA)...OR..ANY SUCH THING IS OBTAINED BY REPLACING X IN THE GIVEN FUNCTION BY 2 OR A OR TANIA OR WHATEVER IT IS .SO F(G(X))MEANS WE HAVE TO PUT G(X) IN PLACE OF X IN F(X)...THIS LEADS TO SOME CONFUSION .SO WE DO IT IN 2 STEPS
1.WE PUT F(G(X))=F(Y)...THAT IS WE PUT G(X)=Y...NOW WE CAN EASILY FIND F(Y).IN THE PRESENT EXAMPLE WE HAVE
F(X)=4X-3...SO F(Y)=4Y-3
2.NOW WE SUBSTITUTE FOR Y,BY FINDING Y FROM Y=G(X)..IN THE PRESENT EXAMPLE
Y=G(X)=SQRT.(2X+3)...SUBSTITUTING IN STEP1.,WE GET
F(G(X))=F(Y)=4Y-3=4{SQRT(2X+3)}-3....THAT IS IT...HOPE YOU GOT IT...
NOW I THINK YOU CAN TRY THE SECOND PROBLEM!!IF IN TOUBLE PLEASE COME BACK

Find h(f(x)) if h(x)=1/x+2 and f(x)=4x-3
Any thing you can provide would be a great assistance to an old woman.