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

$(\frac{g}{f})(-4)=\frac{g(-4)}{f(-4)}$

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

$(\frac{g}{f})(-4)=\frac{g(-4)}{f(-4)}=\frac{72}{36}$

Therefore, the answer is:

$(\frac{g}{f})(-4)=2$