Question

Find the domain and range of f(x) =x^2-49/x-7​

Answer 1

Answer:

Step-by-step explanation:

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(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.