Question

NO LINKS!! Please assist me with this problem Part 3m

If a and h are real numbers, find the following values for the given function ​

Answer 1

Given function

• f(x) = 9x - 3

Find the following

• d) f(a + h) = 9(a + h) - 3
• e) f(a) + f(h) = 9a - 3 + 9h - 3 = 9(a + h) - 6
• f) [f(a + h) - f(a)]/h =

[ 9(a + h) - 3 - 9a + 3]/h =

9h /h = 9

Answer 2

`\textsf{(d)} \quad \boxed{9a+9h-3}`

`\textsf{(e)} \quad \boxed{9a+9h-6}`

`\textsf{(f)} \quad \boxed{9}`

Explanation:

Given function:

`f(x) = 9x - 3`

Part (d)

To find f(a + h), substitute x = a + h into the function:

`\begin{aligned}\implies f(a+h)&=9(a+h)-3\\&=9a+9h-3\end{aligned}`

Part (e)

Find f(a) by substituting x = a into the function:

`\implies f(a)=9a-3`

Find f(h) by substituting x = h into the function:

`\implies f(h)=9h-3`

Therefore:

`\begin{aligned}\implies f(a)+f(h)&=(9a-3)+(9h-3)\\&=9a-3+9h-3\\&=9a+9h-6\end{aligned}`

Part (f)

`\begin{aligned}\implies (f(a+h)-f(a))/(h)&=((9(a+h)-3)-(9a-3))/(h)\\\\&=(9a+9h-3-9a+3)/(h)\\\\&=(9h)/(h)\\\\&=9\end{aligned}`