Find a formula for fg and simplify Let fx 6x 5 and gx x2

Find a formula for fg and simplify. Let f(x) = 6x - 5 and g(x) = x/2. (a) Find a formula for f middot g. Write your answer as a polynomial in standard form. (b) Find a formula for g middot g. Write your answer as a polynomial in standard form. Find functions f(x) and g(x) such that F(x) = 3/x - 1 can be expressed in the form f(g(x)). Is f(x) = x^3 + 8 one-to-one? Why or why not? Let f(x) = 3x/x-2. Find a formula for f^-1(x). A car dealership advertises a 15% discount on all its new cars. In addition, the manufacturer offers a $1000 rebate on the purchase of a new car. Let x represent the sticker price of the car. (a) Suppose only the 15% discount applies. Find a function f that models the purchase price of the car as a function of the sticker price x. (b) Suppose only the $1000 rebate applies. Find a function g that models the purchase price of the car as a function of the sticker price x. (c) Find a formula for H = f middot g. (d) Find H^-1(x). What does this function represent? (e) Find H^-1 (13,000). What does your answer represent?

Solution

8) F(x) = 3 / (x-1)

f(x) = 3 / x

g(x) = x - 1

f (g (x)) = 3 / (x-1)

9) f(x) = x^3 + 8

the function is one to one function if it follows horizontal and vertical line test

if a horizontal and vertical line is drawn on the graph it cuts the graph at only one point

hence its a one to one function

10) f(x) = 3x / (x-2)

y = 3x / (x-2)

switch x and y

x = 3y / (y-2)

xy - 2x = 3y

xy - 3y = 2x

y ( x-3) = 2x

y = 2x / (x-3)

therefore,

f^-1(x) = 2x / (x-3)