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son4ous [18]
3 years ago
10

If f(x) = 2x2 + 1 and g(x) = x2 - 7, find (f + g)(x).​

Mathematics
1 answer:
pishuonlain [190]3 years ago
7 0

Answer:

(f+g)(x) = 3x^{2} - 6

Step-by-step explanation:

First, lets understand what (f+g)(x) means.

(f+g)(x) is when you are taking the values in the function f(x) and adding it to the values in the function g(x).

So, this is what the equation looks like when you substitute the functions in to (f+g)(x):

(f+g)(x) = (2x^{2} +1) + (x^{2}  -7)

Now, combine like terms and Simplify:

(f+g)(x) = 3x^{2} - 6

This is your final answer.

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  x = 5

Step-by-step explanation:

The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.

<h3>Application</h3>

  \dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}

__

<em>Additional comment</em>

Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.

  \log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5

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