She can carry up to 5 books in her backpack
<h3>
Answer: g(x) = 5x+9, second choice</h3>
Explanation:
When we reflect over the vertical y axis, every negative x value becomes positive and vice versa. So we effectively replace x with -x like so
f(x) = -5x+9
f(-x) = -5(-x)+9 ... replace every x with -x
f(-x) = 5x+9
g(x) = 5x+9
A point like (1,4) on f(x) will reflect over to (-1,4) on g(x). If we apply this to every point on f(x), then all of f(x) will reflect to g(x).
Step-by-step explanation:
The given expression is :
![(\sqrt[3]{128} )^x](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B128%7D%20%29%5Ex)
We need to solve the above expression.
According to one of the law of indices,
![(\sqrt[a]{m} )^b=(\sqrt{m})^{b/a}](https://tex.z-dn.net/?f=%28%5Csqrt%5Ba%5D%7Bm%7D%20%29%5Eb%3D%28%5Csqrt%7Bm%7D%29%5E%7Bb%2Fa%7D)
Using above property,
![(\sqrt[3]{128} )^x=(128)^{x/3}\\\\=(64\times 2)^{x/3}\\\\=4(2)^{x/3}\ (\because\ \sqrt{64}=4) \\\\=4(\sqrt[3]{2})^x\\\\=4(2^{1/3})^x](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7B128%7D%20%29%5Ex%3D%28128%29%5E%7Bx%2F3%7D%5C%5C%5C%5C%3D%2864%5Ctimes%202%29%5E%7Bx%2F3%7D%5C%5C%5C%5C%3D4%282%29%5E%7Bx%2F3%7D%5C%20%28%5Cbecause%5C%20%5Csqrt%7B64%7D%3D4%29%20%5C%5C%5C%5C%3D4%28%5Csqrt%5B3%5D%7B2%7D%29%5Ex%5C%5C%5C%5C%3D4%282%5E%7B1%2F3%7D%29%5Ex)
Hence, this is the required solution.
