Question

If k(x) = 5x-6, which expressionis equivalent to (k+ k)(4)?

O5(4+4)-6
O 5(5(4)-6)-6
O 54-6+54-6
O5(4)-6+5(4) - 6

Answer 1

• D) 5(4) - 6 + 5(4) - 6

Given function

• k(x) = 6x - 6

To find

• Equivalent expression of (k + k)(4)

Solution

Use the sum of functions definition:

• (f + g)(x) = f(x) + g(x)

In our case both f and g are represented by k, so the sum of functions is:

• (k + k)(x) = k(x) + k(x)

Substitute the function values to get:

• (k + k)(4) =
• k(4) + k(4) =
• 5(4) - 6 + 5(4) - 6

This is matching the answer choice D

Answer 2

5(4) - 6 + 5(4) - 6

Explanation:

`\textsf{Given}:\quad k(x)=5x-6`

`\begin{aligned}(k+k)(x) & =k(x)+k(x)\\\\\implies (k+k)(4) & =k(4)+k(4)\\& = \left[5(4)-6\right]+\left[5(4)-6\right]\\& = 5(4)-6+5(4)-6\end{aligned}`