let f: R-R, f(x)= x^3 + x -1 find the solution of f(x)= f^-1 (x)

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Q. Let f

:

\to

R be a function such that

f (x) = x^{3} + x^{2} f^{'} (1) + x f^{''} (2) + f^{'''} (3), x \in R

. Then

f (2)

equal?

Find f + g, f - g, $c f (c ϵ R, c \neq 0)$ . fg. $\frac{1}{f}$ and $\frac{f}{g}$ in each of the following :
(i) $f (x) = x^{3} + 1$ and $g (x) = x + 1$
(ii) $f (x) = \sqrt{x - 1}$ and $g (x) = \sqrt{x + 1}$

Q. Let

f : R \to R be f (x) = x^{3} + x^{2} + x - 1

and

g (x) = f^{- 1} (x)

, then

g^{'} (2)

Q. Let f : R − {−1} → R − {1} be given by

f (x) = \frac{x}{x + 1} . Write f^{- 1} (x)

Q. Let f

:

\to

R be defined by

f (x) = ln (x + \sqrt{x^{2} + 1})

, then number of solutions of

| f^{- 1} (x) | = e^{- | x |}

is?

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