Question

Find (f*f)(3)

A
B
C
D

Answer 1

Choice A is correct answer.

Explanation:

We have given a function.

f(x) = x²-x

We have to find composition of function to itself.

(f o f)(x) = ? and (f o f)(3) = ?

The formula to find the composition is:

(f o f)(x) = f(f(x)

Putting given values in above formula, we have

(f o f)(x) = f(x²-x)

(f o f)(x) = (x²-x)² - (x²-x)

(f o f)(x) = x⁴-2x³+x²-x²+x

(f o f)(x) = x⁴-2x³+x

Putting x = 3 in above equation, we have

(f o f)(3) = (3)⁴-2(3)³+(3)

(f o f)(3) = 81 -2(27)+3

(f o f)(3) = 81-54+3

(f o f)(3) = 30 which is the answer.

Answer 2

a. 30

Explanation:

(f.f) = f(f(x))

Given: f(x) = x^2 -x

Now replace x = x^2 -x in f(x), we get

(f.f) = f((x^2 - x)^2 - (x^2 - x))

= (x^2 - x) (x^2 - x) -x^2 + x

= x^4 -x^3 - x^3 + x^2 - x^2 + x

= x^4 -2x^3 + x

Now plug in x = 3

f.f(3) = 3^4 -2(3)^3 + (3)

= 81 - 2*27 + 3

= 81 -54 + 3

f.f(3) = 84 -54

(f.f)(3) = 30

Thank you.