consider the functions f(x)=x^2+4x-1 and g(y)=2y. Calculate the following: f(0), (g of f)(0), (g/f)(0), (f/g)(0), and (f of f) (x)

Question

Math help

Answer 1

1) f(0)=(0)²+4(0)-1=-1

2) g(f(0))=2((0)2+4(0)-1)=-2

 

3) **  Should be zero

4) ** Should be undetermined

 

5) f(f(x))=(x²+4x-1)²+4(x²+4x-1)-1=x⁴+8x³+18x²+8x-4

 

If I understand you correctly for problems 3 and 4 the above should lead you to the solutions I stated in 3 and 4. Hopefully the answers above for 1, 2, and 5, should get you to understand what the process is. You are simply substituting the variable with the given expression to calculate.   

 

 

Answer 2

f(x)= x²+4x-1  g(y)= 2y

 

f(0)= 0² + 4(0) -1 = -1

 

(g of f)(0)= g(f(0))= g(-1)= 2(-1)= -2

 

(g/f)(0)= g(0)/f(0)= 2(0)/-1= 0

 

(f/g)(0)= f(0)/g(0)= -1/0 = undefined

 

(f of f)(x)= f(f(x))= (x²+4x-1)²+ 4(x²+4x-1) -1

Answer 3

f(X) = x²+ 4x - 1                       g(y) = 2y

 

f(0) = 0² + 4(0) -1                        

 

      = -1

 

g(f(0)) = g(-1)

 

           = 2(-1)

 

           = -2

 

(g/f) (0) = g(0) / f(0)

 

             =  0 / -1

 

             = 0

 

(f/g) (0) = f(0) / g(0)

 

             = -1 / 0

 

          Undefined

 

fIf(x))  = f ( x² + 4x -1) 

 

           = ( x² +4x -1)² + 4( x² + 4x -1) -1

 

           = x⁴ +8x³ + 14x² - 8x + 1 + 4x² +  16x -4 -1

 

           = x⁴ + 8x³ + 18x² + 8x