Question

IF F ( X ) = 6+1 then find f ( 2 ) + ( 3 )

Answer 1

Answer:

F(x + 2) = 2F(x) - F(x + 1) ...(i)

Putting x = 0, we get

F(2) = 2F(0) - F(1)

⇒ F(2) = 2(2) - 3

{∵F(0)=2,F(1)=3}

⇒ F(2) = 4 - 3 ⇒ F(2) = 1 Putting x = 1, in eq. (i), we get

F(3) = 2F(1) - F(2)

= 2(3) - 1 {∵F(1)=3,F(2)=1}

⇒ F(3) = 5

Putting x = 2, in eq. (i), we get

F(4) = 2F(2) - F(3)

= 2(1) - 5 {∵F(2)=1,F(3)=5}

⇒ F(4) = - 3

Putting x = 3, in eq. (i), we get

F(5) = 2F(3) - F(4)

= 2(5) + 3 {∵F(3)=5,F(4)=−3}

⇒ F(5) = 13

Step-by-step explanation:

Answer 2

Answer:

Here take y=f(x)

Then y=2x−6

⇒2x=y+6

⇒x=  

2

y

​  

+3

Now switch x and y in the resulting equation. The resulting function of x is the inverse.

⇒y=  

2

x

​  

+3

Thus the inverse function is f  

−1

(x)=  

2

x

​  

+3.

Step-by-step explanation: