Question

1. if f(x)=1-x^2 and g(x)=1-x which is the rule of function (f-g)(x)

A. 1+x
B. -x^2+x
C. -x^2-x+2
D. x^3-x^2-x+1

2. For the pair of functions, f and g, find (f•g)(x) and (g•f)(x).
f(x) = 3+x, g(x) = x^2 + 1
PLEASE HELP

Answer 1

QUESTION 1

If f(x)=1-x² and g(x)=1-x,

Then,

(f-g)(x)=f(x)-g(x)

This implies that,

`( f - g)(x) = 1 - {x}^(2) - (1 - x)`

`( f - g)(x) = 1 - {x}^(2) - 1 + x`

We simplify to get,

`( f - g)(x) = - {x}^(2) + x`

The correct choice is B.

QUESTION 2

Given:

f(x)=3+x

and

`g(x) = {x}^(2) + 1`

`(f\circ g)(x)=f(g(x))`

`(f\circ g)(x)=f( {x}^(2) + 1 )`

`(f\circ g)(x)=3 + {x}^(2) + 1`

`(f\circ g)(x)= {x}^(2) +4`

Also,

`(g\circ f)(x)=g(f(x))`

`(g\circ f)(x)=g( 3+ x)`

`(g\circ f)(x)= {(3 + x)}^(2) + 1`

`(g\circ f)(x)= 9 + 6x + {x}^(2) + 1`

`(g\circ f)(x)= {x}^(2) + 6x + 10`