SOLUTION: If f(x)=1-x^2 and g(x)=x^2-1, then for which of the following values of b does f(3b)+8=g(3b)-8?

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Question 1087693: If f(x)=1-x^2 and g(x)=x^2-1, then for which of the following values of b does f(3b)+8=g(3b)-8?
Answer by ikleyn(52747) About Me  (Show Source):
You can put this solution on YOUR website!
.
If  f(x)=1-x^2  then f(3b) + 8 = 1 - (3b)^2 + 8 = 9 - 9b^2.


If  g(x)=x^2-1  then g(3b) - 8 = (3b)^2 -1 - 8 = 9b^2 - 9.



They ask: at which value of "b" will be

9 - 9b^2 = 9b^2 - 9  ???


Simplify:

18 = 18b^2  ===>  b^2 = 1  ===>  there are rwo solutions: b = 1 and b = -1.


Check.  Check b= 1 first;  f(3b) + 8 = f(3) + 8 = 1 - 3^2 + 8 = 0.
                           g(3b) - 8 = g(3) - 8 = 3^2 - 1 - 8 = 0.   Correct !

        Same for b= -1.

Solved.