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  4. The range of the function y=(( cos -1(3 x-1)/π)+1)2 is

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Q. The range of the function $y=\left(\frac{\cos ^{-1}(3 x-1)}{\pi}+1\right)^2$ is

Inverse Trigonometric Functions

Solution:

$-1 \leq 3 x-1 \leq 1 \Rightarrow 0 \leq x \leq \frac{2}{3} \Rightarrow$ domain is $\left[0, \frac{2}{3}\right]$
when $x =0$ then $y =1 ; x =\frac{2}{3}, y =4$. Hence range is $[1,4]$