Given ƒ(x) = 2×2 − 8, g(x) = x2 + 5x + 6, and h(x) = 2x + 4 find…

Given ƒ(x) = 2×2 − 8, g(x) = x2 + 5x + 6, and h(x) = 2x + 4 find each function. *Acceptable format: An algebraic expressions like x^2+5x+3, without spaces. Put polynomials in standard form, i.e. x^4+3x^3+2x^2+x+1. (ƒ + g)(x) = (ƒ − g)(x) = (ƒ + h)(x) = (g − h)(x) = (ƒg)(x) = (ƒg)(x) = (hƒ)(x) = (gh)(x) = (gh)(x) =

Given ƒ(x) = 2√x + 3 and g(x) = −3x + 1 find each value.

*Acceptable format:

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  • An integer like 5.

ƒ(g(1)) =

g(ƒ(1)) =

ƒ(g(−4)) =

g(ƒ(6)) =

ƒ(g(43)) =

g(ƒ(97)) =

 
 
 
 

Given ƒ(x) = 4x + 3, g(x) = xx + 3 and h(x) = −x2 − 2 find each composite function.

*Acceptable format:

  • An algebraic expressions like x^2+5x+3, without spaces.
  • Put polynomials in standard form, i.e. x^4+3x^3+2x^2+x+1.

ƒ(g(x)) =

g(ƒ(x)) =

ƒ(h(x)) =

 
 
 
 

The cost of carpeting a room is $4 per square yard plus $100. Each square yard is equal to 9 square feet.

*Acceptable format:

  1. Write the function for the cost of carpeting a room with y square yards: C(y) =
  2. Write the function to convert s square feet to square yards: Y(s) =
  3. Compose the functions to create a function to represent the cost of carpeting a room of s square feet: C(Y(s)) =
  4. Find the square footage of a room that costs $380 to carpet: square feet.

 

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