Question

20 Given f(x)= |x) and g(x)- , find the following expressions. (a) (f og)(4) (b) (g of)(2) (c) (of) (d) (g o g)(0) (a) (f o g)( 4(Type an integer or a simplified fraction.)

Answer 1

Answer 2

SOLUTION :

f(x) = | x |   and    g(x) = 20 / (x^2 + 5)

a.

(f o g)(x)

= f(g(x)) 

= | 20 / (x^2 + 5) |

So,

(f o g)(4) 

= | 20 / (4^2 + 5) |

= | 20 / 21 |

= 20 / 21  (ANSWER)

b.

(g o f)(x) 

= g(f(x))

= 20 / (( | x |)^2 + 5)

So,

(g o f)(2)

= 20 / ( 4 + 5)

= 20 / 9  (ANSWER)

c.

(f o f)(x)

= f(f(x))

= | | x | |

= x 

So,

(f o f)(1)

= 1 (ANSWER).

d.

(g o g)(x)

= 20 / [ (20 / (x^2 + 5))^2 + 5 ]

So,

(g o g)(0) 

= 20 / [ 20 / (4^2 + 5)

=  20 / 21 (ANSWER)