Question 190314This question is from textbook Introductory and Intermediate Algebra
: Hi, I just want to know if I did the right thing on my homework.Please help me.
1) Find the domain of each square root of function. Then use the domain to graph the radical function.The graphs are labeled (a) through (f) and are shown in [-10,10,1] by [-10,10,1] viewing rectangles.]
f(x)= square root of 8-2x
Solution:
8-2x <=(less than or equal to) 0
-2x <= -8
x<= 4
The domain of f is{x\x<=4) or (-infinity, 4}
2)Multiply & simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.
sqrt of 5xy multiply by sqrt of 10xy^2
Sol'n:
=sqrt of 5xy.10xy^2
=sqrt of 50x^2y^3
=sqrt of 25x^2y^2 x sqrt of 2y
=5xy sqrt of 2y
3)Add or subtract as indicated. You will need to simplify terms to identify the like radicals,
5 sqrt of 12 + sqrt of 75
Sol'n:
=5sqrt of 4x3 + sqrt of 25x3
=5 x 2 x sqrt of 3 + 5sqrt of 3
=10sqrt of 3 + 5 sqrt of 3
=(10+5)sqrt of 3
= 15sqrt of 3
Please let me know my mistakes...Thanks a lot in advance.
Kattie
This question is from textbook Introductory and Intermediate Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) Find the domain of each square root of function. Then use the domain to graph the radical function.The graphs are labeled (a) through (f) and are shown in [-10,10,1] by [-10,10,1] viewing rectangles.]
f(x)= square root of 8-2x
-----------------------------------------------------
Response:
f(x) = sqrt(8-2x)
8-2x must be greater than or equal to zero for x to be in the Domain
8-2x >= 0
Add 2x to both sides to get a positive "x-term".
2x <= 8
x <= 4
Domain: All Real Numbers less than or equal to 4 ; (-inf,4]
=================================================================
2)Multiply & simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.
sqrt of 5xy multiply by sqrt of 10xy^2
Sol'n:
=sqrt of 5xy.10xy^2
=sqrt of 50x^2y^3
=sqrt of 25x^2y^2 x sqrt of 2y
=5xy[sqrt of 2y]
-----------------------------
Your work is correct.
========================
3)Add or subtract as indicated. You will need to simplify terms to identify the like radicals,
5 sqrt of 12 + sqrt of 75
Sol'n:
=5sqrt of 4x3 + sqrt of 25x3
=5 x 2 x sqrt of 3 + 5sqrt of 3
=10sqrt of 3 + 5 sqrt of 3
=(10+5)sqrt of 3
= 15sqrt of 3
----------
Your work is correct
=============================
Cheers,
Stan H.
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