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pashok25 [27]
3 years ago
9

Are the functions inverse of each other? f(x)=5x^2+3, g(x)sqrt x-3/5

Mathematics
2 answers:
MariettaO [177]3 years ago
8 0

Answer:

  no

Step-by-step explanation:

The function f(x) does not pass the horizontal line test, so has no inverse, except on a restricted domain. The question does not include any restriction on the domain, so the functions are not inverses of each other.

If we assume your functions are ...

  f(x)=5x^2+3\\\\g(x)=\sqrt{\dfrac{x-3}{5}}

Then the value of g(f(x)) is ...

  g(f(x))=\sqrt{\dfrac{(5x^2+3)-3}{5}}=\sqrt{\dfrac{5x^2}{5}}=\sqrt{x^2}

This is only equal to x when x ≥ 0. For x < 0, g(f(x)) ≠ x, so the functions are not inverses.

_____

You can see from the graph that the function g(x) is not the reflection of f(x) across the line y=x. If the functions were inverses, each would be a reflection of the other.

luda_lava [24]3 years ago
3 0

Answer:

No.

Step-by-step explanation:

Plugging in g(x) into f(x), you don't get x. g(x) would need to be = \sqrt{x\frac{-3}{5} }

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6. Write the explicit formula for the geometric sequence of the height of the ball on the 10th bounce.First bounce: 54 inchescom
Nat2105 [25]

The height of the ball initially is 54 inches. The common ratio has been provided which is 0.750.

The explicit formular for the geometric sequence is shown as;

\begin{gathered} ar^{n-1} \\ \text{Where a is the first term in the sequence,} \\ r\text{ is the common ratio betw}een\text{ every successive term} \\ \text{And n is the nth term} \\ \text{The explicit formular for the height of the ball on the 10th bounce is;} \\ ar^{n-1} \\ 54\times(0.750)^{10-1} \\ 54\times(0.750)^9 \\ 54\times0.07508468\ldots \\ 4.0545 \end{gathered}

The explicit formula is shown as;

54 x (0.750)^9

The rest is simply to solve for the height on the 10th bounce

5 0
1 year ago
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Dmitrij [34]
X/1000=72/125  multiply both sides by 1000

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So the fraction is 576/1000
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Answer:

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Step-by-step explanation:

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