Question

Find the first four iterates of the function f(x) = 7x + 2 if X0= 3.
a. 7, 12, 18, 36
C. 3, 23, 47, 81
b. 23, 163, 1143, 8003
d. 23, 76, 114, 208

Answer 1

it’s b 23,163,1143,8003

Answer 2

The first four iterates of the function f(x) are 23, 163, 1143 and 8003

The function is given as:

$f(x) = 7x + 2$

Where:

$x_o=3$

Substitute 3 for x in f(x)

$f(3) = 7 \times 3 + 2$

$f(3) = 23$

Substitute 23 for x in f(x), for the next iteration

$f(23) = 7 \times 23 + 2$

$f(23) = 163$

Substitute 163 for x in f(x), for the next iteration

$f(163) = 7 \times 163 + 2$

$f(163) = 1143$

Substitute 1143 for x in f(x), for the next iteration

$f(1143) = 7 \times 1143 +2$

$f(1143) = 8003$

Hence, the first four iterates of the function f(x) are 23, 163, 1143 and 8003

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