QUESTION 1
If f(x)=1-x² and g(x)=1-x,
Then,
(f-g)(x)=f(x)-g(x)
This implies that,
[tex]( f - g)(x) = 1 - {x}^{2} - (1 - x)[/tex]
[tex]( f - g)(x) = 1 - {x}^{2} - 1 + x[/tex]
We simplify to get,
[tex]( f - g)(x) = - {x}^{2} + x[/tex]
The correct choice is B.
QUESTION 2
Given:
f(x)=3+x
and
[tex]g(x) = {x}^{2} + 1[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x)=f( {x}^{2} + 1 )[/tex]
[tex](f\circ g)(x)=3 + {x}^{2} + 1[/tex]
[tex](f\circ g)(x)= {x}^{2} +4[/tex]
Also,
[tex](g\circ f)(x)=g(f(x))[/tex]
[tex](g\circ f)(x)=g( 3+ x)[/tex]
[tex](g\circ f)(x)= {(3 + x)}^{2} + 1[/tex]
[tex](g\circ f)(x)= 9 + 6x + {x}^{2} + 1[/tex]
[tex](g\circ f)(x)= {x}^{2} + 6x + 10[/tex]
