Range of the function `f(x)=(1+x^2)/(x^2)` is equal to

Options

A. (0,1)
B. [0,1]
C. `(1,oo)`
D. `[1,oo)`

Answer

C

Explanation

We observe that f(x) is defined for all ` x in R -{-0}` .
So, domain (f)=R-{0}
Let ` y=(1+x^(2))/(x^(2))`. Then,
`y=(1+x^(2))/(x^(2))implies pm sqrt((1)/(y-1))`
for x to be real, we must have
`y-1 gt 0 implies ygt 1implies y in (1,oo)`
Hence, range `(f)=(1,oo)`