Question

find the domain of f(x) = √49-x^2​

Answer 1

Answer:

The domain of

f(x)=149−x2−−−−−−√

is established by 49−x2>0 , that is, −7<x<7 .

By symmetry, the function has a minimum at 0 , with f(0)=1/7 . Because of the vertical asymptotes, the range is [1/7,∞) .

This can also be deduced by solving for f(x) : since

49−x2=1(f(x))2

we have

x2=49(f(x))2−1(f(x))2

which is solvable for f(x)≥1/7 , taking into account that f(x)>0 by definition