Write a \"T\" for the statement which you think is true, and Write an \"F\" for

Question

Write a "T" for the statement which you think is true, and Write an "F" for the statement which you think is false. i. If f g: [a, b] rightarrow R are strictly increasing functions, then so is f g. ii. If f g: [a, b] rightarrow R are one-to-one continuous functions, then either f + g is one-to-one or f rightarrow g is one-to-one. iii. Every polynomial function of an even degree defined on R has no inverse function. iv. Every polynomial function of an odd degree defined on R has an inverse function.

Explanation / Answer

From the given question,

i) True

If f and g are strictly increasing, the fg is also increasing.

ii)True

If f and g are strictly continous functions , the either f+g or f-g are strictly continous functions.

iii)True

If f is even function, then it doesnt have inverse for R

iv)False

f(x)=sin(x) is odd function.

Its inverse sin-1(x) is not defined for entire R.

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