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MAT 104 Quiz 21 Solutions, Quizzes of Algebra

Utica CollegeAlgebra

The solutions to quiz 21 for the mat 104 course. It includes step-by-step calculations for solving two algebraic equations and finding the value of 'a' for a given function.

Typology: Quizzes

Pre 2010

Uploaded on 07/28/2009

koofers-user-x9p
koofers-user-x9p 🇺🇸

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MAT 104 Quiz 21
Monday, November 1, 2004
1. Solve 2
x= 3
2
x= 3 =⇒2 = 3x
=⇒x=2
3
2. Solve 3x−2
x+ 1 = 5 −2x+ 1
x−1
3x−2
x+ 1 = 5 −2x+ 1
x−1=⇒(3x−2)(x−1) = 5(x+ 1)(x−1) −(2x+ 1)(x+ 1)
=⇒3x2−5x+ 2 = 5x2−5−(2x2+ 3x+ 1)
=⇒3x2−5x+ 2 = 3x2−3x−6
=⇒ −2x=−8
=⇒x= 4
3. For f(x) = x+1
x−1, find asuch that f(a) = 4.
f(a) = 4 ⇐⇒ a+ 1
a−1= 4
⇐⇒ a+ 1 = 4(a−1)
⇐⇒ a+ 1 = 4a−4
⇐⇒ a=5
3

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Download MAT 104 Quiz 21 Solutions and more Quizzes Algebra in PDF only on Docsity!

MAT 104 Quiz 21

Monday, November 1, 2004

  1. Solve (^2)

x = 3

x = 3^ =⇒^ 2 = 3x =⇒ x =^23

  1. Solve (^3) x − 2

x + 1 = 5^ −^

2 x + 1 x − 1

3 x − 2 x + 1 = 5^ −^

2 x + 1 x − 1 =⇒^ (3x^ −^ 2)(x^ −^ 1) = 5(x^ + 1)(x^ −^ 1)^ −^ (2x^ + 1)(x^ + 1) =⇒ 3 x^2 − 5 x + 2 = 5x^2 − 5 − (2x^2 + 3x + 1) =⇒ 3 x^2 − 5 x + 2 = 3x^2 − 3 x − 6 =⇒ − 2 x = − 8 =⇒ x = 4

  1. For f (x) = x x+1− 1 , find a such that f (a) = 4.

f (a) = 4 ⇐⇒ a a^ + 1− 1 = 4 ⇐⇒ a + 1 = 4(a − 1) ⇐⇒ a + 1 = 4a − 4 ⇐⇒ a =^53