Mathematics Algebra
posted by Dulyana .
Question:
If the expression (x^2 + 2x +4)/(x^2  2x  4) has a value between (1/3) and 3 for all real values of x, determine the range of the expression [9.(3)^x + 6.(3)^2x + 4]/[ 9.(3)^2x  6.(3)^x +4
My thoughts on the question:
I can see that if we substitute x=[3.(3)^x] we can turn the first expression into the one ,which we are told to find the range.But I have no idea on going further..

But (x^2 + 2x +4)/(x^2  2x  4) does not always fit into the interval [1/3,3]. If x is very close to 1±√5 then the value is arbitrarily large
f(3.2) = 129
plus, you have a typo. I think you mean
[9.(3)^2x + 6.(3)^x + 4]/[ 9.(3)^2x  6.(3)^x +4]
using u = 3.3^x
That becomes (u^2+2u+4)/(u^22u4)
so, I guess its range is [1/3,3]
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