You may please answer my question a and b clearly. I would really appreciate it.

Question

You may please answer my question a and b clearly. I would really appreciate it. Thank you.

[05] 1. Consider Domain R and Codomain R, f(r) cos r, g(r) tan ar. a) Answer the following questions for f(r), g(r): f(r) g(r) onto (ii) State a Domain for each function so that each has an Inverse f (r) g(r) (iii) Prove or Disprove: Each function is Onto R. f(T) g(r) b) If g(r) has an Inverse h (z) and r a e Domain of g(r) (i) What is the value of (h o g)(a)? (ii) Using your calculator evaluate (h o g)(2.0943) (iii) What assumption caused the error in the answer to (h o g)(2.0943)?

Explanation / Answer

a)

1) for a function inverse exists if and only if the function is one to one , for cosx function if x value is 90 or 270 degrees both gives the same value (0) in codomain hence no one to one relation . Inverse doesn,t exist .

for tanx it is 0 for both 0 and 180 degrees . henace no one to one relation , inverse doesn't exist

2) the domain should be selected such that every value in the domain should have unique value . By looking ate the cosine graph in the interval -90<x=<90 (degrees, less than or equal to 90) every x has unique value in codomain .

similar concept can be applicable to tanx also the domain should be -90<x<90 ( degrees, strictly less than).

3) onto function is a function where each element of codomain has a pre image in domain .

for cos x function the range is restricted between 1 and -1 so it is not onto

for tanx it is onto because it covers whole range of values ( by graph ,it extends from positive infinty to negative infinty)

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