SOLUTION: Hello. I did not find how to solve this problem in the Blitzer College Algebra Book. Here is the problem, which I have not been prepared to solve (no examples had been shown in the

Algebra ->  Functions -> SOLUTION: Hello. I did not find how to solve this problem in the Blitzer College Algebra Book. Here is the problem, which I have not been prepared to solve (no examples had been shown in the      Log On


   

Question 1136338: Hello. I did not find how to solve this problem in the Blitzer College Algebra Book. Here is the problem, which I have not been prepared to solve (no examples had been shown in the book, very frustrating ad antipedagogical!)
Let f(x)= x^2 - x + 4 and g(x) = 3x - 5. Find g(1) and f(g(1)).
Please, show me the steps and if possible w/ explanations so that Imay understand how to solve this type of problems. Thanks
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f%28g%28x%29%29=%283x-5%29%5E2-%283x-5%29%2B4-------------simplify this; and then evaluate it for x=1. (That would be for the second part of your question. You can still find g(1) separately, again g%281%29=3%2A1-5.)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Hello. I did not find how to solve this problem in the Blitzer College Algebra Book. Here is the problem, which I have not been prepared to solve (no examples had been shown in the book, very frustrating ad antipedagogical!)
Let f(x)= x^2 - x + 4 and g(x) = 3x - 5. Find g(1) and f(g(1)).
Please, show me the steps and if possible w/ explanations so that Imay understand how to solve this type of problems. Thanks
g(x) = 3x - 5
g(1) = 3(1) - 5 ------- Substituting 1 for x 
g(1) = 3 - 5
g(1) = - 2

matrix%281%2C3%2C+f%28g%281%29%29%2C+%22=%22%2C+f%28-+2%29%29 ----- Substituting - 2 for g(1)
matrix%281%2C3%2C+f%28x%29%2C+%22=%22%2C+x%5E2+-+x+%2B+4%29
matrix%281%2C3%2C+f%28-+2%29%2C+%22=%22%2C+%28-+2%29%5E2+-+%28-+2%29+%2B+4%29
matrix%281%2C5%2C+f%28-+2%29%2C+%22=%22%2C+4+%2B+2+%2B+4%2C+%22=%22%2C+10%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Tutor @MathTherary just explained you how to do it technically.

            I only want to add to it the general approach description: 


First step  :  You calculate  g(1) by substituting x= 1 into the formula for g(x);


Second step :  Then you calculate  f(g(1)) by substituting the found value ( the number)  g(1)  into the given formula for f(x).



Both steps are extremely simple !



It may seem to be complicated, but when you do it one-two times, it becomes trivial !