Question

Find the inverse of this function:
f(x) = 3 - 2tan(0.5x)
I'm not really sure how to do this...
I've tried y = 3 - 2tan(0.5x)
and rearranging to make x the subject

Answer 1

can u first isolate the tan(0.5x) term from
y=...?

Answer 2

-2tan(0.5x)=y-3
tan(0.5x)=(y-3)/(-2)?

Answer 3

correct,

when tan y = z, then y= arctan z

so, tan 0.5x = (y-3)/(-2)
0.5 x = arctan [(y-3)/(-2)]
got this ?

Answer 4

What exactly is arctan?

Answer 5

its the inverse tan function.
for details, look wiki

Answer 6

Oh its the inverse, we never learnt that term in new zealand lol.
So
x = 2 arctan[(y-3)/(-2)]?

Answer 7

yes, correct...
you can write that as
2 arctan[(3-x)/(2)] also
which is your inverse function

Answer 8

Thanks so much!!! You seem to be the most active person on here lol.

Answer 9

there are many others active here too :)
and welcome ^_^