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aschool2000
27.02.2021 •
Mathematics
(7).Given f(x) =
![\frac{1}{x ^{2} - 1}](/tpl/images/2183/2151/d3d65.png)
and g(x)=
where x & R.
Find the ;
(i). inverse of g(x) (ii). Expression
iii). Largest domain of f(x) and g(x) respectively.
Solved
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Ответ:
The inverse of g(x) is![g^{-1}(x)=\frac{2x}{1-x}](/tpl/images/1153/2581/8b95b.png)
The domain of g(x) is (-∞,-2)U(-2,∞)
The domain of f(x) is (-∞,-1)U(-1,1)U(1,∞)
Step-by-step explanation:
Find the inverse of g(x).
Solve for x
Find the domain of g(x)
Numerator and denominator have domain
(-∞,∞).
However, g(x) is undefined if the denominator is 0. Hence, x=-2 must be taken out of the domain. So, the domain of g(x) is
(-∞,-2)U(-2,∞).
Find the domain of f(x)
The numerator and denominator have the domain
(-∞,∞)
However, f(x) is undefined if the denominator is 0. This rules out +1 and -1. So, the domain of f(x) is
(-∞,-1)U(-1,1)U(1,∞)
I am not sure what you mean for (ii).
Ответ:
Well, volume is: length x width x height
so, 5 x 14 x 8= 560 inches