If a function is even, then f(-x) = x.
If a function is odd, then f(-x) = -x.
y = x³ + x² → f(x) = x³ + x² → -f(x) = -(x³ + x²) = -x³ - x²
f(-x) = (-x)³ + (-x)² = [(-1)(x)]³ + [(-1)(x)]² = (-1)³x³ + (-1)²x²
= -1x³ + 1x² =-x³ + x²
f(-x) ≠ f(x) and f(-x) ≠ -f(x)
y = x³ + x² is not odd and not even
Answer: neither
*im sorry but I cant see the bottom number but I'll consider it as x
tan 45° = 3/x
x = 3/tan45
x is 3
hope this helps :)
Answers and explanations:
87. The domain of added functions includes the restrictions of both. So the range of the added function in this question is [-4, 3]
88. When finding the domain of a divided function we do the same as adding, but with an extra rule: g can't equal zero. So for this question the domain is (-4, 3)
89. To graph f + g you add the y-values for each x-value. I added a picture to help explain this one!
Let the digit in the tens place be x
tens place = x (therefore the value is 10x)
ones place = x + 7
The number is 10x + x + 7
Add 26 to it
10x + x + 7 + 26 = 11x + 33
It is 5 times the sum of the digit
11x + 33 = 5(x + x + 7)
11x 33 = 10x + 35
x = 2
x+ 7 = 2 + 7 = 9
So the number is 29
