Question

Given f(x) = 5x² - 4 and g(x) = 6 - 1/2x², find the following expressions. 

Answer 1

Answer 2

SOLUTION :

f(x) = 5x^2 - 4   and    g(x) = 6 - 1/2 x^2

a.

(f o g)(x)

= f(g(x)) 

= 5(6 - 1/2 x^2)^2 -  4 

So,

(f o g)(4) 

= 5(6 - 1/2 * 4^2)^2 - 4  

= 20 - 4

= 16 (ANSWER)

b.

(g o f)(x) 

= g(f(x))

= 6 - 1/2(5x^2 - 4)^2

So,

(g o f)(2)

= 6 - 1/2(5(2)^2 - 4)^2

= 6 - 128

= - 122 (ANSWER)

c.

(f o f)(x)

= f(f(x))

= 5(5x^2 - 4)^2 - 4

So,

(f o f)(1)

= 5(5(1)^2 - 4)^2 - 4

= 1 (ANSWER).

d.

(g o g)(x)

= 6 - 1/2(6 - 1/2 x^2)^2

So,

(g o g)(0) 

= 6 - 1/2(6 - 0)^2

= - 12 (ANSWER)