Answer to Question #256959 in Calculus for junior

Question

1. A plant grows 1.67 cm in its first week. Each week it grows by 2% more than it did the week before. By how much does it grow in twenty weeks, including the first week?

2.  Two functions f and g are defined on the set R, of real numbers by

f:x-> 2x - 3 or f:x-> 2x-3/x

x

and

g : x -> 1- 3x OR g:x-> 1- 3x/2 Find the inverse of the function f and the domain of gof.

2

Answer 1

1.The length of a plant each week form an geometric sequence with $b{\scriptscriptstyle 1}=1.67$ and q = 1.02

We have to find the sum of the first 20 elements of this sequence. The formula of the first n elements is:

$S{\scriptscriptstyle n}={\frac{b{\scriptscriptstyle 1}*(1-q^{n})} {1-q}}$

In our case: $S{\scriptscriptstyle 20}={\frac{1.67*(1.02^{20}-1)} {1.02-1}} = 124.07$ cm

2. f:x-> 2x - 3

f(x) = 2x-3. To find it inverse we should express x in terms of f(x): $x={\frac{f(x)+3} 2}$

The inverse of this function is $f^{-1}: x\to{\frac{x+3} 2}$

g : x -> 1- 3x

(gof)(x) = 1-3(2x-3) = 1-6x+9. The domain of this function is x є R