Question

Find (f*f)(0)
f(x)=x2-1

Answer 1

Choice b is correct answer.

Explanation:

We have given a function.

f(x) = x²-1

We have to find the composition of function to itself.

(fof)(x) = ? and (fof)(0) = ?

(fof)(x) = f(f(x))

Putting values in above formula, we have

(fof)(x) = f(x²-1)

(fof)(x) = (x²-1)²-1

(fof)(x) = x⁴-2x²+1-1

(fof)(x) = x⁴-2x²

Now, Putting x = 0 in above equation , we have

(fof)(0) = (0)⁴-2(0)²

(fof)(0) = 0-0

(fof)(0) = 0 which is the answer.

Answer 2

B

Explanation:

( f o f)(­ 0) means to substitute x=0 into a new expression created by substituting f(x) into f(x).

`f(f(x)) = (x^2-1)^2-1\\f(f(x)) = x^4-2x^2+1-1\\f(f(x)) = x^4 -2x^2`

Now substitute x=0 into the expression
`x^4 - 2x^2`.

`0^4 - 2*0^2\\0-0\\0`

The answer is 0.