Question

Match each operation involving f(x) and g(x) to its answer

Answer 1

(g-f) (-1)=
`√(15)`

(f/g)(-1)= 0

(g+f)(2) =
`√(3)-3`

(g*f)(2) =
`-3 √(3)`

Explanation:

Given :

`f(x)=1-x^2\\g(x)=√(11-4x)`

To find :
`(g-f)(-1)`

Solution :

`g(x)-f(x)=√(11-4x)-1+x^2\\(g-f)(x)=√(11-4x)-1+x^2\\(g-f)(-1)=√(11+4)-1+1=√(15)`

To find :
`\left ( (f)/(g) \right )(-1)`

Solution :

`(f(x))/(g(x))=(1-x^2)/(√(11-4x))\\(f(-1))/(g(-1))=(1-1)/(√(11+4))=0`

To find :
`(g+f)(2)`

Solution:

`g(x)+f(x)=√(11-4x)+1-x^2\\(g+f)(x)=√(11-4x)+1-x^2\\(g+f)(2)=√(11-8)+1-4=√(3)-3`

To find:
`(g* f)(2)`

Solution:

`g(x)f(x)=(gf)(x)=√(11-4x)(1-x^2)\\(gf)(2)=√(11-8)(1-4)=-3√(3)`

Answer 2

(g-f) (-1)= sqrt(15)

(f/g)(-1)= 0

(g+f)(2)=sqrt(3)-3

(g*f)(2)=-3*sqrt(3)

Explanation:

We have to eval the expressions given in the point indicated.

Lets start by the first equation

(g-f)(-1)= g(-1) - f(-1)=
`√(11-4*(-1))    - 1 +(-1)^(2)` =
`√(15)`

Now, lest continue with the others

(f/g)(-1)= f(-1)/g(-1)= (1-1)/sqrt(15)=0

(g+f)(2)=g(2)+f(2)=sqrt(3)-3

(g*f)(2)=g(2)*f(2)=sqrt(3)*(-3)=-3sqrt(3)