Answer:
N. -104
S. 112
O. -59
Explanation:
i will try my best to solve all of them, but may set up some problems that are ready to be solved.
N. Find (f + g)(8) what this question means is to find the function of f and g added together. the 8 is equal to x, so you will first combine the functions f and g together, and then we will worry about 8
f(x) =3x+4 and g(x) = -2x²-4 (f+g)(x) is the same as the functions f and g added together:
(3x + 4) + (-2x²-4) = -2x² + 3x
now we will set x = 8 and solve
(f+g)(8)= -2(8)² + 3(8) --> -2(64) + 24 = -104 < this is our answer for (f+g)(8)
S. Find (f × g)(-4) this is similar to the above problem, except it is multiplication. we will solve for (f*g) first
f(x) = x + 2 and g(x) = x³-2x
(f×g)(x) = (x+2)(x³-2x) <-- use FOIL to solve and we get:
x^4 + 2x³ - 2x² - 4x and now we subtitute -4 for x
(f×g)(-4) = (-4)^4 + 2(-4)³ - 2(-4)² - 4(-4) = 112 < this is our answer for (f*g)(-4)
O. Find (f - g)(4) again, similar to the above problems besides the sign
f(x) = 4x-3 and g(x) = x³+2x
(f - g)(x) = (4x - 3) - (x³ + 2x) <-- remember to distribute the negative sign in front of x³ + 2x, or else you will not get the correct answer
this is equal to: -x³+2x-3 and now we put x = 4
-(4)³ + 2(4) -3 = -59 < this is our answer for (f - g)(4)
edit: was able to add the answers
I. Find (f×g)(1)I will set this problem up for you because I have done a similar problem for S
f(x) = x²+4 + 2x and g(x) = -3x+2
(f×g)(x) = -3x³-4x² - 8x + 8<-- x = 1 in this equation, so solve for that and you should have your answer
W. Find (f+g)(10) again, I will set this problem up for you again since there is a similar problem for N
f(x) = 3x+3 and g(x) = -4x+1
(f+g)(x) = 3x+3 + (-4x+1) = -x + 4<-- x = 10 in the equation and you just have to plug in the value 10 for x and that would be the answer
B. says I have swear words in this answer, but the answer is -16, please let me know if you would like an explanation for this question
H. Find(f × g)(-4)i will solve this problem entirely instead of setting it up like the last similar one
f(x) = 2x - 1 and g(x) = 3x - 3
(f×g)(x) = (2x-1)(3x-3) = 6x² - 9x + 3 <-plug in -4 for x
(f×g)(-4) = 6(-4)² -9(-4) + 3 = 135 <this is our answer for (f*g)(-4)
K.Find (f×g)(-1) i will solve this problem as well
f(x) = x²+3 and g(x)=4x-3
(f×g)(x) = (x²+3)(4x-3) = 4x³ - 3x² + 12x - 9
(f×g)(-1) = 4(-1)³ - 3(-1)² + 12(-1) - 9 = -28 <answer for (f×g)(-1)
T. Find f(g(2))the meaning of this is f composed of g, it can also be stylized as (fºg). this means that the x value of the function g is 2, and the solution to the function g is the x value of the function f. so lets solve this:
f(x) = 3x+2 and g(x) = 2x² + 5 we will solve g(2) first
g(2) = 2(2)² + 5 = 2(4) + 5 = 8 + 5 = 13so g(2) = 13
now we plug the solution to g(2) into f(x)
f(13) = 3(13)+2 = 39 + 2 = 41 <this is our answer to f(g(2))