Question

How do I evaluate the following from B through D?

Answer 1

Part B.

In this case, we need to evaluate the following function,

`(g-f)(-3)=g(-3)-f(-3)`

Then, by replacing the number -3 into the place of x in functions f and g, we have

`g(-3)=8-(-3)^3=8-(-27)=8+27=35`

and

`f(-3)=(-3)^2-5(-3)=9+15=24`

Then,

`(g-f)(-3)=g(-3)-f(-3)=35-24=11`

Therefore, the answer is:

`(g-f)(-3)=11`

Part C.

In this case, we need to evaluate

`(f\cdot g)(1)=f(1)\cdot g(1)`

So, by replacing the number 1 into the place of x in function f and g , we have

`f(1)=(1)^2-5(1)=1-5=-4`

and

`g(1)=8-(1)^3=8-1=7`

Then, we have that

`(f\cdot g)(1)=f(1)\cdot g(1)=(-4)\cdot7=-28`

Therefore, the answer is:

`(f\cdot g)(1)=-28`

Part D.

Similarly, in this case we have

`((g)/(f))(-4)=(g(-4))/(f(-4))`

By replacing the number -4 into the place of x in functions f and g ,we get

`g(-4)=8-(-4)^3=8-(-64)=8+64=72`

and

`f(-4)=(-4)^2-5(-4)=16+20=36`

So, we have that

`((g)/(f))(-4)=(g(-4))/(f(-4))=(72)/(36)`

Therefore, the answer is:

`((g)/(f))(-4)=2`