Non-empty Domain

Algebra Level 3

If set $X$ denotes the domain of two functions $f(x)=8x, g(x)=2x^3,$ how many nonempty sets $X$ are there such that $f=g?$

9 8 10 7

1 solution

Mietantei Conan
Mar 1, 2014

For $f=g$ ; $8x = 2x^3$ There are $3$ values of $x$ namely $-2$ , $0$ and $2$ which satisfy this equation. The number of sub sets is given by $2^n$ where $n$ is the number of elements in a set. In our case $n$ is $3$ . Therefore number of subsets is $8$ but empty set is not included so our answer is $7$ .

Non-empty Domain

1 solution

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