Answer:
f(g(x))=(x-2)^2 - 7
(x-2)(x-2) - 7
x^2-2x-2x+4-7
x^2-4x-3
g(f(x))=x^2-2-7
x^2-9
(x+3)(x-3)
Step-by-step explanation:
- to solve for f(x), replace x with the g(x).
- since we don't multiply a bracket with the negative or the positive signs to the
- exponent, you have to factor into two binomials.
- use the FOIL method to eliminate the brackets.
- add like-terms
- to find g(x), replace x with the f(x).
- add like-terms
- since there's difference of square, factor them into two binomials
Answer:
3
+9x-30
Step-by-step explanation:
Multiply the three into each number
3
+9x-30
Answer:
- x = 0 or 1
- x = ±i/4
- x = -5 (twice)
Step-by-step explanation:
Factoring is aided by having the equations in standard form. The first step in each case is to put the equations in that form. The zero product property tells you that a product is zero when a factor is zero. The solutions are the values of x that make the factors zero.
1. x^2 -x = 0
x(x -1) = 0 . . . . . x = 0 or 1
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2. 16x^2 +1 = 0
This is the "difference of squares" ...
(4x)^2 - (i)^2 = 0
(4x -i)(4x +i) = 0 . . . . . x = -i/4 or i/4 (zeros are complex)
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3. x^2 +10x +25 = 0
(x +5)(x +5) = 0 . . . . . x = -5 with multiplicity 2
The inequality is a > 12, which means a is greater than 12. This means that we are looking for numbers that are greater than 12 to place into the solution set. Options A and B are incorrect because 10 and 11 are both numbers less than 12, respectively. Option D is also incorrect because the inequality specifies that the numbers in the solution must be greater than 12, not equal to it, so 12 is not a solution.
This leaves option C as the correct answer, because all of the solutions in the set (13, 14, and 15) are greater than 12.
Therefore, your answer is C.
Hope this helps!