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Let f (x) = log2(x) + 2 and g(x) = log2(x3) – 4.

Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points)

Part B: Determine the solution to the system of nonlinear equations. (6 points)

Respuesta :

MrRoyal

The function h(x) in its simplest form is [tex]h(x) = 4log_2(x)- 2[/tex]

The functions are given as:

[tex]f(x) = log_2(x) + 2[/tex]

[tex]g(x) = log_2(x^3) - 4[/tex]

(a) Function h(x)

This is given as:

[tex]h(x) = f(x) + g(x)[/tex]

So, we have:

[tex]h(x) = log_2(x) + 2 + log_2(x^3) - 4[/tex]

Collect like terns

[tex]h(x) = log_2(x) + log_2(x^3)+ 2 - 4[/tex]

[tex]h(x) = log_2(x) + log_2(x^3)- 2[/tex]

Apply law of logarithm

[tex]h(x) = log_2(x \times x^3)- 2[/tex]

[tex]h(x) = log_2(x^4)- 2[/tex]

Apply law of logarithm

[tex]h(x) = 4log_2(x)- 2[/tex]

Hence, function h(x) in its simplest form is [tex]h(x) = 4log_2(x)- 2[/tex]

(b) System of nonlinear equations

The equations are not given.

So, the question cannot be solved

Read more about composite functions at:

https://brainly.com/question/10687170

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