For function f(x) = (x − 1)³ and g(x) = 1-6x ,value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
As given,
Given function :
f(x)=(x − 1)³
g(x)=1-6x
The value of following functions are:
a.(f ∘ g)(x)
=f(g(x))
=f(1-6x)
=(1-6x -1)³
=(-6x)³
=-216x³
b. (g ∘ f)(x)
= g(f(x))
=g(x − 1)³
=1 -6(x − 1)³
=1 -6(x³ -3x² +3x -1)
=-6x³+18x² -18x+7
c. f(f(x))
=f(x-1)³
=((x-1)³ -1)³
=(x³ -3x² +3x -1-1)³
=(x³ -3x² +3x -2)³
d. f²(x)= (f · f)(x)
=f(x) × f(x)
=(x-1)³ × (x -1)³
=(x -1)⁶
Therefore, for function f(x) = (x − 1)³ and g(x) = 1-6x ,the value of following function is:
a. (f ∘ g)(x)=-216x³
b. (g ∘ f)(x)=-6x³+18x²-18x+7
c. f(f(x))=(x³ -3x² +3x -2)³
d. f²(x)=(x-1)⁶
The complete question is:
For function f(x) = (x − 1)³ and g(x) = 1-6x find the value of the following.
a. (f ∘ g)(x)
b. (g ∘ f)(x)
c. f(f(x))
d. f²(x)= (f · f)(x)
Learn more about function here
brainly.com/question/12431044
#SPJ1
