Answer:
[tex](g\cdot f)(0)=4[/tex]
Step-by-step explanation:
So we have the two functions:
[tex]f(x)=5x-4\text{ and } g(x)=x^2-1[/tex]
And we want to find:
[tex](g\cdot f)(0)[/tex]
This is the same as:
[tex]=g(0)\cdot f(0)[/tex]
So, find g(0) and f(0):
g(0):
Substitute 0 into g(x):
[tex]g(0)=(0)^2-1[/tex]
Square:
[tex]g(0)=0-1[/tex]
Subtract:
[tex]g(0)=-1[/tex]
And f(0):
Substitute 0 into f(x):
[tex]f(0)=5(0)-4[/tex]
Multiply:
[tex]f(0)=0-4[/tex]
Subtract:
[tex]f(0)=-4[/tex]
So, our equation is now:
[tex](g\cdot f)(0)=g(0)\cdot f(0)=(-1)\cdot(-4)[/tex]
Multiply:
[tex]=4[/tex]
So, our answer is 4.
And we're done!
