# What is the range of #f(x) = ln(sin^(-1)(x^2+x+3/4))# ?

##### 1 Answer

Jun 15, 2017

#### Explanation:

Given:

#f(x) = ln(sin^(-1)(x^2+x+3/4))#

First note that:

#x^2+x+3/4 = x^2+x+1/4+1/2 = (x+1/2)^2+1/2#

which can take any value in the range

The domain of

So the possible valid arguments to it in

#[1/2, oo) nn [-1, 1] = [1/2, 1]#

#sin^(-1)(1/2) = pi/6#

#sin^(-1)(1) = pi/2#

and

So the range of

Hence the range of

#[ln(pi/6), ln(pi/2)]#