Respuesta :

Answer:

(a)7x+7h-9

(b)7h

(c)7

Explanation:

Given f(x) defined below:

[tex]f\mleft(x\mright)=7x-9[/tex]

Part A

[tex]\begin{gathered} f\mleft(x+h\mright)=7(x+h)-9 \\ =7x+7h-9 \end{gathered}[/tex]

Part B

[tex]\begin{gathered} f\mleft(x+h\mright)-f\mleft(x\mright)=\lbrack7x+7h-9\rbrack-\lbrack7x-9\rbrack \\ =7x+7h-9-7x+9 \\ =7x-7x+7h-9+9 \\ =7h \end{gathered}[/tex]

Part C

Taking the result from Part B:

[tex]\begin{gathered} \frac{f\mleft(x+h\mright)-f\mleft(x\mright)}{h}=\frac{7h}{h} \\ =7 \end{gathered}[/tex]

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