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**Unformatted text preview: **Topics in Functions Answers
x+2
6
x+3
(b) f −1 (x) =
5
−1 (x) = − 5 x +
(c) f
3 (i) f −1 (x) = 3 − 1. (a) f −1 (x) = (d) f −1 (x) = (x − √ 1
3
2)2 + 5, x ≤ 2 1
(e) f −1 (x) = 3 (x − 5)2 + 1 , x ≥ 5
3
1
(f) f −1 (x) = 1 x5 + 3
3
√
(g) f −1 (x) = 5 + x + 25 (h) f −1 (x) = − x+5
3 −4 √ x+4 (j) f −1 (x) = − x+1 , x > 1
2
4x − 3
(k) f −1 (x) =
x
x
−1 (x) =
(l) f
3x + 1
4x + 1
(m) f −1 (x) =
2 − 3x
6x + 2
(n) f −1 (x) =
3x − 4
−3x − 2
(o) f −1 (x) =
x+3 3. Given that f (0) = 1, we have f −1 (1) = 0. Similarly f −1 (5) = 1 and f −1 (−3) = −1 5.3 Other Algebraic Functions 5.3 311 Other Algebraic Functions This section serves as a watershed for functions which are combinations of polynomial, and more
generally, rational functions, with the operations of radicals. It is business of Calculus to discuss
these functions in all the detail they demand so our aim in this section is to help shore up the
requisite skills needed so that the reader can answer Calculus’s call when the time comes. We
brieﬂy recall the deﬁnition and some o...

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