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photoshop1234 [79]
2 years ago
7

Yx -³ / 3x⁰ Please help!!

Mathematics
2 answers:
Dafna1 [17]2 years ago
6 0
Hey, i’d love to help you but there seems to be a typo in your equation because a minus sign (or negative sign) can’t be raised to the power of 3.
Marat540 [252]2 years ago
4 0

I'll assume you meant yx^(-3) over 3x^0.

Rewrite this as:


  y

-----------------

x^3*3*x^0


Note that x^3 * x^0 = x^(3+0) = x^3, so that we are left with


 y

------- is the simplest possible answer

x^3


Note that x^0 = 1

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We're given the following function:
f(x)=log(.75^x)=log[  (\frac{3}{4}) ^{x}]=log( \frac{3^x}{4^x})

In order to see if the function is decreasing we'll take its derivative. If \frac{d}{dx}f(x)\ \textgreater \ 1 the function is increasing, if \frac{d}{dx}f(x)\ \ \textless \  \ 1 the function is decreasing.

We take the derivate:
\frac{d}{dx}[log( \frac{3^x}{4^x})]= \frac{4^x}{3^x}[ \frac{d}{dx} (\frac{3^x}{4^x})]=\frac{4^x}{3^x} \frac{4^x[ \frac{d}{dx} (3^x)]-3^x[ \frac{d}{dx} (4^x)]}{ 4^2^x}=
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Which implies the function is decreasing.

Another way to answer the problem (although less insightful) you can take any two real numbers k and q such that k\ \textgreater \ q, then if f(k)-f(q)\ \textgreater \ 0 the function is increasing and if f(k)-f(q)\ \textless \ 0 the function is decreasing. You can verify the function is decreasing with any two numbers in the function's domain.
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