Answer:
5x+31
Step-by-step explanation:
f(g(x))
5(x+7) -4
5x+35-4
5x+31=f(g(x))
Step-by-step explanation:
for any matrix multiplication number of columns of first matrix should be equal to number of rows of second matrix.
For AB
A has 3 columns and B has 3 rows so it matches . Hence can be multiplied.
For BA
B has 2 columns and A has 2 rows it also matches so can be multiplied
So you want to find two numbers that add up to -13 and multiply to
40. You can find the factors of 40 and find the pair that adds up to
-13. -8 and -5 multiply to 40 and add up to -13.
<span><span>(x−5)</span><span>(x−8)</span>=<span>x2</span>−13x+40</span>
You can use foil to test it
<span><span>x2</span>+<span>(−8x)</span>+<span>(−5x)</span>+40=<span>x2</span>−13x+40</span>
<span><span>x2</span>−13x+40=<span>x2</span>−13x+</span>
For this case we have to, by defining properties of powers and roots the following is fulfilled:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
We must rewrite the following expression:
![\sqrt [3] {8 ^ {\frac {1} {4} x}}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B8%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B4%7D%20x%7D%7D)
Applying the property listed we have:
![\sqrt [3] {8 ^ {\frac {1} {4} x}} = 8 ^ {\frac{\frac {1} {4} x} {3} }= 8 ^ {\frac {1} {4 * 3} x} = 8 ^ {\frac {1} {12} x}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B8%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B4%7D%20x%7D%7D%20%3D%208%20%5E%20%7B%5Cfrac%7B%5Cfrac%20%7B1%7D%20%7B4%7D%20x%7D%20%7B3%7D%20%7D%3D%208%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B4%20%2A%203%7D%20x%7D%20%3D%208%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B12%7D%20x%7D)
Using the property again we have to:
![8 ^ {\frac {1} {12} x} = \sqrt [12] {8 ^ x}](https://tex.z-dn.net/?f=8%20%5E%20%7B%5Cfrac%20%7B1%7D%20%7B12%7D%20x%7D%20%3D%20%5Csqrt%20%5B12%5D%20%7B8%20%5E%20x%7D)
Thus, the correct option is option C
Answer:
Option C
