Answer:
Simplifying
6x + -3 = 21 + -2x
Reorder the terms:
-3 + 6x = 21 + -2x
Solving
-3 + 6x = 21 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
-3 + 6x + 2x = 21 + -2x + 2x
Combine like terms: 6x + 2x = 8x
-3 + 8x = 21 + -2x + 2x
Combine like terms: -2x + 2x = 0
-3 + 8x = 21 + 0
-3 + 8x = 21
Add '3' to each side of the equation.
-3 + 3 + 8x = 21 + 3
Combine like terms: -3 + 3 = 0
0 + 8x = 21 + 3
8x = 21 + 3
Combine like terms: 21 + 3 = 24
8x = 24
Divide each side by '8'.
x = 3
Simplifying
x = 3
Step-by-step explanation:
Answer:
2/4
Step-by-step explanation:
Answer:
a) and d) are bijections. b) and c) are not
Step-by-step explanation:
a) Every linear non constant function is a bijection. We can easily find the inverse of f by making a simple calculus.
If y is on the function image, we have y = -3x + 4 for certain x, then
y- 4 = -3x
-(y-4)/3 = x
therefore
b) -3 * X² + 4 is not a bijection because quadratic funtions arent bijective. If you evaluate in opposite values you will obtain the same result. For example f(-1) = f(1) = 6
c) (x+1)/(x+2) is not a bijection. It isnt even defined in -2 because the denominator is equal to 0 if X= -2 and we cant divide by 0. A bijective function from R to R must be defined in every element of R. In general, homographic non linear functions are not bijective for the same reason this function is not.
d) is bijective. There isnt a simple argument we can use to conclude this. We have no other choice than trying to find the inverse function by making a calculus.
Y =
Y-1 =
Not that since 5 is odd, we can calculate independently of which value Y-1 takes. Therefore , and we can conclude that f is bijective.
I hope this helps you!