given ( f(x)=9x + 4 ),\n(a) find ( f(x + h) ) and simplify.\n(b) find ( \frac{f(x + h)-f(x)}{h} ) and…

given ( f(x)=9x + 4 ),\n(a) find ( f(x + h) ) and simplify.\n(b) find ( \frac{f(x + h)-f(x)}{h} ) and simplify.\npart: ( 0 / 2 )\npart 1 of 2\n(a) ( f(x + h)= )

given ( f(x)=9x + 4 ),\n(a) find ( f(x + h) ) and simplify.\n(b) find ( \frac{f(x + h)-f(x)}{h} ) and simplify.\npart: ( 0 / 2 )\npart 1 of 2\n(a) ( f(x + h)= )

Answer

Explanation:

Step1: Find ( f(x + h) )

Substitute ( x+h ) into ( f(x)=9x + 4 ). ( f(x + h)=9(x + h)+4 ) Expand the expression: ( f(x + h)=9x+9h + 4 )

Step2: Find ( \frac{f(x + h)-f(x)}{h} )

First, substitute ( f(x + h)=9x+9h + 4 ) and ( f(x)=9x + 4 ) into ( \frac{f(x + h)-f(x)}{h} ). [ \begin{align*} \frac{f(x + h)-f(x)}{h}&=\frac{(9x+9h + 4)-(9x + 4)}{h}\ &=\frac{9x+9h + 4-9x - 4}{h}\ &=\frac{9h}{h} \end{align*} ] Cancel out ( h ) (assuming ( h\neq0 )): ( \frac{9h}{h}=9 )

Answer:

(a) ( f(x + h)=9x + 9h+4 ) (b) ( \frac{f(x + h)-f(x)}{h}=9 )