hey lads, i just was wondering if i solved this right:(adsbygoogle = window.adsbygoogle || []).push({});

5. Consider the function f(x) = 3x+cos(x), defined on the interval [0, pi]

(a) prove that f has an inverse function g. Note: you are note expected to find the inverse function g indicate your reasoning.

I dre the graph of f(x) and showed its a one to one function with a horizontal line test... Im not sure this is enough please tell me if i have to do anything extra

then i said that any continuos 1 to 1 function has a inverse function with the change of domain and range...

(b) determine the domain and range of the funcion g

since the function domain was A and range B, the inverse domain is B and range A.

function = d [0,pi] r [1,8.421]

inverse = d[1,8.4] r [0,pi]

(c) determine the derivative g'(3pi/2) Hint: first, show that f(xo) = 3(pi/2) when x0 = pi/2

find the derivative of the function at xo then the derivative of the inverse is 1/derivativefunction

is all my reasoning right? im sure illl have this on my final, any advice appreciated

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# Inverse Functions. Test Prep help.

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