Calculus 1 problem

Question

Let f(x) = cos^-1 (sqrt ((3x)/(1-3x)))

Find the domain and range of this function. Plot the graph.

Is for one to one in its domain? Explain this by solving y=f(x) for x

Write down the inverse function of f. What is its domain and range? Can you graph it using the graph of f(x)?

Answer 1

Plot sqrt(3x/(1-3x)) to see that it is real valued only for 0 ≤ x ≤ 1/3 and it takes values between 0 and 1 only for x ≤ 1/6.

 

arccos(x) is defined only for -1 ≤ x ≤ 1

 

therefore, the domain of the given function is 0 ≤ x ≤ 1/6; the range is 0 ≤ y ≤ π/2

 

I think I will leave the rest of the problem for you to work out.