Question

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

a) m = 0
b) b = 0
c) m = 5
d) m = 1

Answer 1

For the given equation 5f(x) = f(5), the value of m that satisfies the equation is m = 0.

Step-by-step explanation:

In the given equation, we have 5f(x) = f(5). Let's substitute f(x) with its equation mx + b: 5(mx + b) = m(5) + b.

Expanding the equation gives us 5mx + 5b = 5m + b. Since f(5) = mx + b, we can simplify the equation to get 5mx + 5b = mx + b.

Now, we can compare the coefficients of m and b on both sides of the equation. We have 5m on the left side and m on the right side. This implies that 5m = m.

To solve for m, we can subtract m from both sides, which gives us 5m - m = 0. Simplifying further, we get 4m = 0. Dividing both sides by 4, we find that m = 0. Therefore, the correct answer is option a) m = 0.