For any linear function f(x)=mx+b, when does 5f(x)=f(5x)+5?

a: when b = 0 b: when b = 5/4

c: when b = 5 d: always

The correct option is b).

Step-by-step explanation:

Given :

f(x) = mx + b  ---  (1)

5f(x) = f(5x) + 5  --- (2)

Solution :

When we replace x by 5x in equation (1) we get,

f(5x) = 5mx + b --- (3)

Now in equation (2) put the values of f(x) and f(5x) we get,

5mx + 5b = 5mx + b + 5

4b = 5

Therefore the correct option is b).

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Step-by-step explanation:

f(x)=m x+b

5 f(x)=5 (m x+b)=5 m x+5 b

f(5x)+5=5 m x+b

as 5 f(x)=f(5x)+5

5 m x+5 b=5 mx +b +5

5b =b+5

4 b=5

b=5/4