Question

1) f(x) = 2x + 1 f(2), f(- 3), f(1), (0), f(2) 2) f(x) = - x + 1 f(- 1) , f(- 2) , f(3), (0), f(3)3) f(x) = - (x + 3) f(1) , f(0), f(3), (4) f(- 1) 4) f(x) = - 3(x + 3) + 2 f(2), f(- 3), f(1), (0), f(2)5) f(x) = 5/(x - 5) f(2) , f(- 3) , f(1), (0), f(2) 6) f(x) = 2/(2x - 5) f(2) , f(- 3) f(1), (0), f(2) ​

Answer 1

Ответ:

1) f(2)=2•2+1=4+1=5

f(-3)=2•(-3)+1=-6+1=-5

f(1)=2•1+1=2+1=3

f(0)=2•0+1=0+1=1

2) f(-1)=-(-1)+1=1+1=2

f(-2)=-(-2)+1=2+1=3

f(3)=-(3)+1=-3+1=-2

f(0)=-(0)+1=0+1=1

3) f(1)=-(1+3)=-(4)=-4

f(0)=-(0+3)=-(3)=-3

f(3)=-(3+3)=-(6)=-6

f(4)=-(4+3)=-(7)=-7

f(-1)=-(-1+3)=-(2)=-2

4) f(2)=-3(2+3)+2=-3•5+2=-15+2=-13

f(-3)=-3(-3+3)+2=-3•0+2=0+2=2

f(1)=-3(1+3)+2=-3•4+2=-12+2=-10

f(0)=-3(0+3)+2=-3•3+2=-9+2=-7

5) f(2)=5/(2-5)=5/(-3)=-1⅔

f(-3)=5/(-3-5)=5/(-8)=-⅝

f(1)=5/(1-5)=5/(-4)=-1¼

f(0)=5/(0-5)=5/(-5)=-1

6) f(2)=2/(2•2-5)=2/(4-5)=2/(-1)=-2

f(-3)=2/(2•(-3)-5)=2/(-6-5)=2/(-11)=-2/11

f(1)=2/(2•1-5)=2/(2-5)=2/(-3)=-⅔

f(0)=2/(2•0-5)=2/(-5)=-⅖

Answer 2

To solve these equations, we need to substitute the given values into the functions and evaluate the expressions.

Let's go through each equation one by one:

1) f(x) = 2x + 1 - f(2): Substitute x = 2 into the function: f(2) = 2(2) + 1 = 4 + 1 = 5 - f(-3): Substitute x = -3 into the function: f(-3) = 2(-3) + 1 = -6 + 1 = -5 - f(1): Substitute x = 1 into the function: f(1) = 2(1) + 1 = 2 + 1 = 3 - f(0): Substitute x = 0 into the function: f(0) = 2(0) + 1 = 0 + 1 = 1 - f(2): Substitute x = 2 into the function: f(2) = 2(2) + 1 = 4 + 1 = 5

2) f(x) = -x + 1 + f(-1) - f(-1): We are not given the value of f(-1) in the question. Without this value, we cannot evaluate the function for any input.

3) f(x) = -(x + 3) - f(1): Substitute x = 1 into the function: f(1) = -(1 + 3) = -4 - f(0): Substitute x = 0 into the function: f(0) = -(0 + 3) = -3 - f(3): Substitute x = 3 into the function: f(3) = -(3 + 3) = -6 - f(4): Substitute x = 4 into the function: f(4) = -(4 + 3) = -7 - f(-1): Substitute x = -1 into the function: f(-1) = -(-1 + 3) = -2

4) f(x) = -3(x + 3) + 2 - f(2): Substitute x = 2 into the function: f(2) = -3(2 + 3) + 2 = -3(5) + 2 = -15 + 2 = -13 - f(-3): Substitute x = -3 into the function: f(-3) = -3(-3 + 3) + 2 = -3(0) + 2 = 0 + 2 = 2 - f(1): Substitute x = 1 into the function: f(1) = -3(1 + 3) + 2 = -3(4) + 2 = -12 + 2 = -10 - f(0): Substitute x = 0 into the function: f(0) = -3(0 + 3) + 2 = -3(3) + 2 = -9 + 2 = -7 - f(2): Substitute x = 2 into the function: f(2) = -3(2 + 3) + 2 = -3(5) + 2 = -15 + 2 = -13

5) f(x) = 5/(x - 5) - f(2): Substitute x = 2 into the function: f(2) = 5/(2 - 5) = 5/(-3) = -5/3 - f(-3): Substitute x = -3 into the function: f(-3) = 5/(-3 - 5) = 5/(-8) = -5/8 - f(1): Substitute x = 1 into the function: f(1) = 5/(1 - 5) = 5/(-4) = -5/4 - f(0): Substitute x = 0 into the function: f(0) = 5/(0 - 5) = 5/(-5) = -1 - f(2): Substitute x = 2 into the function: f(2) = 5/(2 - 5) = 5/(-3) = -5/3

6) f(x) = 2/(2x - 5) - f(2): Substitute x = 2 into the function: f(2) = 2/(2(2) - 5) = 2/(4 - 5) = 2/(-1) = -2 - f(-3): Substitute x = -3 into the function: f(-3) = 2/(2(-3) - 5) = 2/(-6 - 5) = 2/(-11) = -2/11 - f(1): Substitute x = 1 into the function: f(1) = 2/(2(1) - 5) = 2/(2 - 5) = 2/(-3) = -2/3 - f(0): Substitute x = 0 into the function: f(0) = 2/(2(0) - 5) = 2/(-5) = -2/5 - f(2): Substitute x = 2 into the function: f(2) = 2/(2(2) - 5) = 2/(4 - 5) = 2/(-1) = -2

Please note that for equation 2, we cannot evaluate the function without knowing the value of f(-1).