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astraxan [27]
3 years ago
11

Given f(x) = 5x + 7,g(x) = 3x-1 find f(g(x))

Mathematics
1 answer:
kakasveta [241]3 years ago
7 0

Answer:

f(g(x)) = 15x + 2

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Distributive Property

<u>Algebra I</u>

  • Functions
  • Function Notation
  • Composite Functions

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

f(x) = 5x + 7

g(x) = 3x - 1

<u>Step 2: Find</u>

  1. Substitute in functions:                                                                                    f(g(x)) = 5(3x - 1) + 7
  2. [Distributive Property] Distribute 5:                                                                 f(g(x)) = 15x - 5 + 7
  3. [Addition] Combine like terms:                                                                        f(g(x)) = 15x + 2
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Answer:

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The given function is

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According to the first principle of the derivative,

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The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

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y-0.25=-0.25(x-2)

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y=-0.25x+0.75

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

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