f(5x)=5f(x) Write an equation for the linear function f satisfying the given conditions.

Answer 1

We are given that f(x) is linear equation. Therefore:

f(x) = mx + b       (From standard form of a linear equation)

From this:

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

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

Now, set 5f(x) = f(5x):

5mx + 5b = 5mx + b

5b = b (Subtract 5mx from each side.)

4b = 0 (Subtract b from each side.)

b = 0 (Duvide each side by 4.)

Therefore, 5 f(x) = f(5x) for any line with b = 0

Here are some sample solutions:



f(x) = x

f(x) = 2x

f(x) = 3x