given $f(x)=4x - 7$,\n(a) find $f(x + h)$ and simplify.\n(b) find $\frac{f(x + h)-f(x)}{h}$ and…

given $f(x)=4x - 7$,\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 $f(x)=4x - 7$,\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)=4x - 7 ). ( f(x + h)=4(x + h)-7 ) Expand the expression: ( f(x + h)=4x+4h - 7 )

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

First, ( f(x + h)=4x + 4h-7 ) and ( f(x)=4x - 7 ) Then ( f(x + h)-f(x)=(4x + 4h-7)-(4x - 7) ) Simplify the numerator: ( 4x + 4h-7 - 4x + 7=4h ) So ( \frac{f(x + h)-f(x)}{h}=\frac{4h}{h} ) Cancel out ( h ) (assuming ( h\neq0 )): ( \frac{4h}{h}=4 )

Answer:

(a) ( f(x + h)=4x + 4h-7 ) (b) ( \frac{f(x + h)-f(x)}{h}=4 )