SOLUTION: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show s

Click here to see ALL problems on Quadratic Equations

Question 30206: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work
Suppose g(x) = x2 + 1 and h(x) = 2x - 1.
a. What is (g◦h)(2)?
b. Express f(x) = (g◦h)(x) algebraically as a single expression.

Found 2 solutions by sdmmadam@yahoo.com, dewtig:
Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website!
Suppose g(x) = x2 + 1 and h(x) = 2x - 1.
a. What is (g◦h)(2)?
b. Express f(x) = (g◦h)(x) algebraically as a single expression.
g(x) = x^2 + 1 ----(1)
h(x) = 2x - 1. ----(2)
a. What is (g◦h)(2)?
(g◦h)(2)= g(h(2))
=g(2X2-1) using x= 2 in (2)
=g4-1)
=g(3)
=3^2+1 using x = 3 in (1)
=9+1 = 10
Therefore (g◦h)(2)= 10
Express f(x) = (g◦h)(x)
f(x) = (goh)(x)
=g(h(x))
=g(2x-1) using (2)
=g(t) where t = (2x-1)----(*)
= t^2+1 using (1)
= (2x-1)^2+1
=[(2x)^2-4x+1]+1 (using (a+b)^2 = a^2+2ab+b^2 and here a = 2x and b = 1)
=4x^2-4x+2

Answer by dewtig(1) (Show Source):
You can put this solution on YOUR website!
Suppose g(x) = x2 + 1 and h(x) = 2x - 1.
a. What is (g◦h)(2)?
b. Express f(x) = (g◦h)(x) algebraically as a single expression.
g(x) = x^2 + 1 ----(1)
h(x) = 2x - 1. ----(2)
a. What is (g◦h)(2)?
(g◦h)(2)= g(h(2))
=g(2X2-1) using x= 2 in (2)
=g4-1)
=g(3)
=3^2+1 using x = 3 in (1)
=9+1 = 10
Therefore (g◦h)(2)= 10
Express f(x) = (g◦h)(x)
f(x) = (goh)(x)
=g(h(x))
=g(2x-1) using (2)
=g(t) where t = (2x-1)----(*)
= t^2+1 using (1)
= (2x-1)^2+1
=[(2x)^2-4x+1]+1 (using (a+b)^2 = a^2+2ab+b^2 and here a = 2x and b = 1)
=4x^2-4x+2