Question

For the functions f(x) = x+2 and g(x) = x^2 - 3 which expression has the greatest value?
A. f(g(1))
B. f(g(-2))
C. g(f(-4))
D. g(f(-2))

2. Find g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3
A. 9
B.8
C.329
D.536

Answer 1

The expression which has the greatest value is; Choice B: f(g(-2))

The value of g(f(-4)) when f(x)= 4x+5 and g(x) = 4x^2 -5x - 3 is; 586

The value of functions

Question 1;

From the information given;

• g(f(x)) = x²+4x +1

• f(g(x)) = x² -1.

Hence, from the options given; upon substitution, it follows that the expression with the greatest value is;

• f(g(-2)) = (-2)² -1 = 4-1 = 3.

Question 2;

From the task content;

• g(f(x)) = 64x² + 140x + 122

Hence, upon substitution of -4 into the function;

• g(f(-4)) = 64(-4)² + 140(-4) + 122

• g(f(-4)) = 586

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