Given f (9) = 2, f' (9) = 6, g (9) = -1, and g' (9) = 8, find the values of the following. (a) (b) (fg)' (9) = Number (§)')= Number

Q: The average classroom teacher's salary is given by f(x) = 975.06x + 32,906.42, where x is the number…

A: Step 1:Step 2:

Q: Given that g(x) =x², find each of the following. a) g(3) b) g(- 3) c) g(-x) d) g(2y) e) g(2 +h)

A: (e) Find the                           Explanation: Given that,

Q: given two functions  p(x) = 2x, q(x) = 3x2 -5   Find: a) (q◦p)(-1) b) (p◦q) (X)

A:

Q: Given f(x) = 23 10x, evaluate the following. (a) (f of-)(42) = (b) (f o f)(40) = %3D

A: First we will calculate the inverse of f. Then see that the composition of f and f inverse works…

Q: If f (2) = 5, g (4) = 2, how much is (f◦g) (4)?

A: Fοg (x)= F (g(x))

Q: 6. Given E[X + 4] = 10 and E (X + 4)°| = 116, determine (a) Var (X + 4), (b) E [X], and (c) Var (X).

A: (a).  Var(X+4) = 116 - 100 = 16  answer   (b).  E[X] = 10 - 4 = 6  answer

Q: Given f(x) = 8x and g(x) = 9x + 1, find the following expressions. (a) (fo g)(4) (b) (g o f)(2) (c)…

A: Composition of functions

Q: Given the functions f (x) = 3x + 5 = (x) 6 g (x) = 4 – x2 and h (x) = = 1 *, find each of the -…

A:

Q: if h(x)=x2-6, find h-1(x)

A: To find the inverse of the function, use the below steps. Replace h(x) by y, so we get y = x2 - 6

Q: write down the power seires for (x)(f(x))

A:

Q: What happens to this base function that went from  a(x)= x2 to  h(x) = -x2+ 4 and why it happened?

A: The objective of the question is to understand the transformation of the base function a(x) = x^2 to…

Q: , find and simplifyf"(x)- Given 3 f(x) = (2x – 1)2

A: Answer

Q: exp(x) = ex ?  Is it just a matter of notation, or does exp( ) mean something else?

A: Yes this is true exp(x) = e^x  exp(x) is command in coding language to type e^x

Q: find the derivative of the func N 4+22

A: Step 1:Step 2: Step 3: Step 4:

Q: Given f(x) = -> (1-3x), what is the value of F (-4)

A: Given f(x)=1-3xWe need to find the value of f(-4)

Q: Evaluate each of the following expressions using the given table of values 2 (a) f(g(-1)) 1 2 (a)…

A: x-2-1012f(x)-10-21-1g(x)210-10The values of different functions at different inputs are given

Q: If f(14)=27, find f-1(27)

A: If f(x) = y is any function and f is one-one then, => f-1(y)=x

Q: For f(x)=4xand g(x)=x+5 find the following. a.(f◦g)(x)                            b.(g◦f)(x)…

A:

Q: Given the functions f(x)=x²-x, g(x)=√x 14. (g-f)(A) find expressions for the following:

A: The given functions  and .The aim is to find the expression for .