Can you please check my answers for these questions? I'm having a little trouble with my signs, because I sometimes substitute in wrong, so I get these wrong because of that, Thank you!


For the following problems, use f(x) = x^2+ 3;
g(x) = –3x; h(x) = 8x - 5;

a. (f + h)(x) = [My answer= x^2+8x-2]

b. (g – h)(x) = [My answer= -11x+5]

c. (f + g)(3) = [My answer= 3]

d. (f ∘ g)(–2) = [My answer= 39]

e. (fg)(2x) = [My answer= -24x^3-18x]

all ok

good work

Sure! Let's go through each question one by one:

a. To find (f + h)(x), you need to add the functions f(x) and h(x) together. So, substitute the function values for f(x) and h(x), and then simplify the expression:
(f + h)(x) = f(x) + h(x) = (x^2 + 3) + (8x - 5) = x^2 + 8x - 2

Your answer of x^2 + 8x - 2 is correct!

b. To find (g - h)(x), you need to subtract the function h(x) from g(x). So, substitute the function values for g(x) and h(x), and then simplify the expression:
(g - h)(x) = g(x) - h(x) = (-3x) - (8x - 5) = -3x - 8x + 5 = -11x + 5

Your answer of -11x + 5 is correct!

c. To find (f + g)(3), you need to substitute 3 in place of x in the expression (f + g)(x). So, substitute the function values for f(x) and g(x), and then simplify the expression:
(f + g)(3) = f(3) + g(3) = (3^2 + 3) + (-3 * 3) = 9 + 3 - 9 = 3

Your answer of 3 is correct!

d. To find (f ∘ g)(-2), you need to first find g(-2) and then substitute that value in place of x in the expression f(x). So, substitute -2 in place of x in g(x), then substitute that result in f(x), and simplify the expression:
(g ∘ f)(-2) = f(g(-2)) = f(-3 * -2) = f(6) = 6^2 + 3 = 36 + 3 = 39

Your answer of 39 is correct!

e. To find (f * g)(2x), you need to first find g(2x) and then substitute that value in place of x in the expression f(x). So, substitute 2x in place of x in g(x), then substitute that result in f(x), and simplify the expression:
(f * g)(2x) = f(g(2x)) = f(-3 * 2x) = f(-6x) = (-6x)^2 + 3 = 36x^2 + 3

Your answer of -24x^3 - 18x is incorrect. The correct answer is 36x^2 + 3.

I hope this helps! Let me know if you have any other questions or need further explanations.