If f(x)=3x-2 and g(x)=x^2+1, find f(g(-1)) and g(f(3))

Step-by-step explanation:

We know the definition of both functions: , and

A) In order to evaluate what , let's first investigate what g(-1) is using the definition for this function:

Now let's find what f(2) is using f(x) definition:

B) In order to evaluate what , let's first investigate what f(3) is using the definition for this function:

Now let's find what g(7) is using the definition for this function:

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this