Mathematics: Given the function f ( x ) = 2 x + 8 , evaluate and simplify the expressions below. See special instructions on how to enter your answers.

Given the function f ( x ) = 2 x + 8 , evaluate

gatornathan79

31.01.2022

f(a) = 2a + 8

f(x + h) = 2x + 2h + 8

$\frac{f(x + h) - f(x)}{h} = 2$

Step-by-step explanation:

Given

f(x) = 2x + 8

Required

f(a)

f(x + h)

$\frac{f(x + h) - f(x)}{h}$

Solving for f(a)

Substitute a for x in the given parameter

f(x) = 2x + 8 becomes

f(a) = 2a + 8

Solving for f(x+h)

Substitute x + h for x in the given parameter

f(x + h) = 2(x + h) + 8

Open Bracket

f(x + h) = 2x + 2h + 8

Solving for $\frac{f(x + h) - f(x)}{h}$

Substitute 2x + 2h + 8 for f(x + h), 2x + 8 fof f(x)

$\frac{f(x + h) - f(x)}{h}$ becomes

$\frac{2x + 2h + 8 - (2x + 8)}{h}$

Open Bracket

$\frac{2x + 2h + 8 - 2x - 8}{h}$

Collect Like Terms

$\frac{2x - 2x+ 2h + 8 - 8}{h}$

Evaluate the numerator

$\frac{2h}{h}$

Hence;

$\frac{f(x + h) - f(x)}{h} = 2$

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