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MAXImum [283]
1 year ago
13

F(x) = 3x-1 , (f of g)(x) = x^2 , Find g(x)

Mathematics
1 answer:
fomenos1 year ago
6 0

Answer:

g(x)=\dfrac{x^2+1}{3}

Step-by-step explanation:

<u>Given functions</u>:

\begin{cases}f(x)=3x-1\\(f \circ g)(x)=x^2\end{cases}

Composite functions are when the <u>output</u> of one function is used as the <u>input</u> of another.

Therefore, the given <u>composite function</u> (f o g)(x) means to <u>substitute</u> function g(x) in place of the x in function f(x).

\begin{aligned}(f \circ g)(x) & = x^2\\f(g(x)) & = x^2\\\implies 3(g(x))-1 & = x^2\\3(g(x))-1+1 & = x^2+1\\3(g(x))&=x^2+1\\\dfrac{3(g(x))}{3}&=\dfrac{x^2+1}{3}\\\implies g(x)&=\dfrac{x^2+1}{3}\end{aligned}

Therefore:

\boxed{g(x)=\dfrac{x^2+1}{3}}

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Answer:

A

Step-by-step explanation:

A is the correct answer because the equation matches option A.

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The minus sign in -2 1/2 shows that the submarine descended and then descended again with the addition sign. Though the addition sign can mean that it ascended its incorrect.

With the equation in hand, we can prove that option A is correct.

If the submarine descended 2 1/2 miles then here must be a minus sign next to the 2 1/2. But if it ascended then there would've been an addition sign to show that it ascended. The other value - 3 1/4 also shows that it ascended with the help of the addition sign.

Ascends - values increase from smallest to highest.

Descends - values decrease from highest to smallest.

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<u>Amplitude</u>
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<u>Period</u>
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<u>Phase Shift</u>
<u>-C</u> = <u>-π</u> = ≈ 1.57<u>
</u> B      2<u>
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