Week Five Assignment

MAT222: Intermediate Algebra

Instructor: Tracy Abram

June 26, 2013

Compassion and Inverse

We will be working the following functions:

1. f (x) = 2x+5 2. g (x) = x2 -3 3. H (x) 7-x3

We have been asked to compute (f-h) (4)

To solve the functions we plug in the correct figures f(x)=2(4)+5 = 8+5 =13 =f(4) = 13 h(x)= 7-4 3 = 33 = 1 h(4)=1

(f-4)(4) = 13-1=12 this is our answer

Compose two pair into each other

A. (f*g)(x)=f (g(x)) f(x2-3)( F IS NOW WORKING ON THE RULE OF G) = 2(x2-3)+5 (THE RULE OF F IS APPLIED TO G) = 2x2-6+5 (SIMPIFIED) =2x2-1 (FINAL ANSWER)

B. (h*g)(x)= h(g(x)) h(x2+5)(THE RULE OF H IS WORKING ON G) = 7-(x2-3)3 (THE RULE OF H IS APPLIED TO G)= 4-x23 (FINAL ANSWER)

C. Inversion of the functions f(x)= 2x+5 (REPLACE WITH Y) y=2x+5 (SWITCH THE Y WITH X) x=2y+5 (SUBTRACT 5 FROM BOTH SIDES) x-5= 2y (DIVIDE BOTH SIDES BY 2) x-52 = y or y = x-52 (PRESENT IN INVERSE FUNTION) f-1(x)=x-52 h(x)=7-x3 (REPLACE WITH Y) y= 7-x3 (SWITCH THE Y WITH X) x= 7-y3 (MULTIPLY BOTH SIDES BY 3) 3x=7-y (SUBTRACT 7 FROM BOTH SIDES) 3x-7=y or y= 3x-7 (PRESENT IN INVERSE FUNTION) h-1(x) =