Answer: The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2
Solution
f(x)=2x+1
y=f(x)
y=2x+1
Isolating x: Subtracting 1 both sides of the equation:
y-1=2x+1-1
y-1=2x
Multiplying both sides of the equation by 1/2:
(1/2)(y-1)=(1/2)2x
(1/2)y-1/2=x
x=(1/2)y-1/2
Changing "x" by "f^(-1) (x)" and "y" by "x":
f^(-1) (x) = (1/2)x-1/2
Answer:
The value of k is -11
Step-by-step explanation:
If (x+2) is a factor of x3 − 6x2 + kx + 10:
Then,
f(x)=x3 − 6x2 + kx + 10
f(-2)=0
f(-2)=(-2)³-6(-2)²+k(-2)+10=0
f(-2)= -8-6(4)-2k+10=0
f(-2)= -8-24-2k+10=0
Solve the like terms:
f(-2)=-2k-22=0
f(-2)=-2k=0+22
-2k=22
k=22/-2
k=-11
Hence the value of k is -11....
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