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Unformatted text preview: r < 1 or r > 1.  7. Let f ( x ) = x 3 + x + 1. (a) Show that f ( x ) is invertible. (b) Compute g (3) where g is the inverse function to f .  8. Find all values of x which satisfy the following inequalities. (a) 2 x x-1 > 1 (b) 2 x | x-1 | > 1 MATA26Y page 2  9. Let f ( x ) = | x-1 | -1. State the hypotheses and conclusion of Rolle’s theorem and explain why this f ( x ) does not contradict the theorem even though f (0) = 0, f (2) = 0, and there is no z in (0 , 2) for which f ( z ) = 0. (You may accept the preceding statement about the derivative of f as fact; you do not have to prove it.)  10. Let f ( x ) = 1 x-1 . (a) Find the linear approximation L ( x ) based at x = 3 to f ( x ) . (b) Find an interval (3-h, 3+ h ) containing 3 throughout which the error in ap-proximating f ( x )by its linear approximation based at x = 3 is less than 0 . 001....
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