if f(g(x)) = x and g(f(x)) = x, and f(x) passes through the point (5,-7), and g'(-7) = -2/3, then find the value of f'(5).

1 answer:

5 0

So it is given that f(x) and g(x) are inverse of each other.

Then f(5) = -7 and hence g(-7) = 5

Now let's use f( g( x ) ) = x

Now take deviation. Use chain rule:

f'( g(x) ) g'( x ) = 1

Plug in x = -7

f'( g( -7 ) ) g'( -7 ) = 1

f'( g( -7 ) ) · -2/3 = 1

f'( g( -7 ) ) = -3/2

f'( 5 ) = -3/2

Hope this helps.

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Consider the sequence 3, 6, 12, 24, 48, .... (a) Write a recursive rule to represent the sequence. (b) Write an explicit rule to

saveliy_v [14]

Answer:

a. a[1] = 3; a[n] = 2a[n-1]

b. a[n] = 3·2^(n-1)

c. a[15] = 49,152

Step-by-step explanation:

Each term of the given sequence is 2 times the previous term. (This description is the basis of the recursive formula.) That is, the terms of the given sequence have a common ratio of 2. This means the sequence is geometric, so the formulas for explicit and recursive rules for a geometric sequence apply.

The first term is 3, and the common ratio is 2.

The recursive rule is ...

a[1] = 3

a[n] = 2×a[n-1]

The explicit rule is ...

a[n] = a[1]×r^(n-1)

a[n] = 3×2^(n-1)

The 15th term is ...

a[15] = 3×2^(15-1) = 3×2^14

a[15] = 49,152

5 0

3 years ago