Question

Composition of Functions and Inverses:Question 7Which expression represents f(f(x)) if f(x) = x2 – 1? A. 2x ^2-2 B. X^4-2x^2+1C. XD. X^4-2x^2

Answer 1

To solve the question, we will follow the steps below:

`f(x)=x^2-1`

To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1

That is:

f((fx)) = (x²-1)² - 1

Then we open the parenthesis

f(f(x)) = (x² - 1)(x² -1) - 1

=x²(x²-1)-1(x²-1) - 1

= x⁴ - x² - x² + 1 - 1

= x⁴ - 2x²

So the correct option is option D. which is x⁴ - 2x²