help with f(x) = tan^-1x from -10≤x≤10?

Question

When it comes to calculus, domain and range confuse the heck outta me! Could someone explain/help me with this problem?

f(x) = tan^-1x from -10≤x≤10

Also, I need to find f^-1(x). Aaaah help!!

Thank you!

Answer 1

what do u need to find? the range of f(x)?
for that, u must remember how the graph of tan(x) looks like. it rises from 0 to infinity for x=0 to x=90 degress. same in the negative side, it falls from 0 to minus infinity for x=0 to x=-90 degress.

thus, your range will simply be the value of tan^-1(-10) to tan^-1(10).

also, f^-1(x) = f^-1(tan^-1(x))=tan(x)

Answer 2

Well clearly, your domain is defined as:
-10
the domain of tan is usually -pi/2
so the range of inverse tan would be the same, but with y, instead of x.

the inverse of inverse tangent would be tangent.

Answer 3

inv tan x (oldstyle is arctan x) has a range from -π/2 to π/2. If you limit the domain to [-10,10], then the range is [arctan -10, arctan 10] = [-1.4711,1.4711].

since invtan x in the inverse of tan x, its inverse is tan x. That's what inverses ARE.

Answer 4

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