iven the following functions f(x) and g(x), evaluate (f∘g)(0). Enter answers using exact values. f(x)=-x^2+2x-1 g(x)=-2/3x+1

Question

Find (f∘g)(0)=

Please reply with answer

Answer 1

Because you didn't use parenthesis on g(x), it's hard to know if it is

or but I'm going to guess the first one.

(f∘g)(0) means f(g(0)) so the first step is to determine g(0) and then plug the results into f(x).

Because g(x) = -(2/3)x + 1, g(0) = -(2/3)(0) + 1 = 1

Because f(x) = -x² + 2x - 1, then f(g(0)) = f(1) = -(1)² + 2(1) - 1 = -1 + 2 - 1 = 0

Answer 2

(F o G)(x) Indicates a composite of two functions, and is read F of G of x. First you want to solve for g(0) in order to simplify the algebra for solving the composite. g(0) = -(2/3)(0) + 1 = 1. You know want to substitute the value for g(0) into f(x) such that x = g(0) = 1. Evaluating f(g(0)) or f(1) we get -(1)^2 + 2(1) - 1 or 0

Answer 3

g(0) = -2/(3(0)+1) =-2

f(g(0) = f(-2) = -4+(2)(-2) -1 = -9

That's by treating -2/3x + 1 as if parentheses were around 3x+1, but as written -2/3(0) = - infinity. -Infinity -1 is still - infinity. then f(g(0) = f( - infinity) = -- ( -infinity) squared + 2(-infinity) - 1 = -(infinity squared). Odds are tho, you left out the parentheses. Infinity^2 > infinity. It has higher cardinality. Anything divided by 0 is + or - infinity.

Answer 4

f(x) = -x² + 2x - 1 and g(x) = -2/(3x+1)

(f o g)(0) = f(g(0)) = f(-2) = - (-2)² + 2(-2) - 1 = -9