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kari74 [83]
4 years ago
10

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

r answers.

Mathematics
1 answer:
sergij07 [2.7K]4 years ago
4 0

Answer:

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}

2

Hence;

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

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