What is f(5) if f(1) = 3.2 and f(x + 1) = 5/2 (f(x))?

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math.

Given that

f(1) = 3.2

f(x + 1) = 5/2 (f(x)) ---1

Substitution x as 1 in equation 1, we get

Then f(2) will be:

f(2) = 5/2 f(1)

= 5/2 × 3.2

= 8

Similarly:

f(3) = 5/2 f(2)

= 2.5 ( 8 ) = 20

f(4) = 5/2 f(3)

= 5/2 × 20

= 50

f(5) = 5/2 f(4)

= 5/2 × 50

= 125

Therefore, f(5) is 125.

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What is f(5) if f(1) = 3.2 and f(x + 1) = 5/2 (f(x))?

Summary:

If f(1) = 3.2 and f(x + 1) = 5/2 (f(x)), f(5) is 125.