The functions f and g are defined for x R by f x a x g x x ax b, where a and b are constants Given that fg(1) 1 and gf(1) 1, find the values of a and b

Question: The functions f and g are defined for x R by f: x a x g: x x + ax +

The functions f and g are defined for x ∈ R by
f: x ↦ a − x g: x ↦ x² + ax + b, where a and b are constants.
Given that fg(−1) = −1 and gf(−1) = −1, find the values of a and b.

Step by Step Solution

★★★★★

3.38 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER To find the values of a and b we need to use the given conditions fg... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Complete Pure Mathematics Questions!

The functions f and g are defined for x R by f: x 4x a g: x b + ax where a and b are constants. Given that f (1) = 2 and g (1) = 3, find the values of a and b.

Functions f and g are defined on R by f (x) := x + 1 and g (x) := 2 if x 1 and g(1) := 0. lim g (f(x) g (lim f(x))

The functions f and g are defined for x R by f: x 4x 1 g: x 2x + k. Find the value of k for which fg = gf.

The functions f and g are defined for x R by f: x 10x + x g: x 2x 1. Express fg(x) in the form a(x + b) + c, where a, b and care constants.

The functions f and g are defined for x R by f: x 2x 1 g: x x + x. Express gf(x) in the form a(x + b) + c, where a, b and care constants.

4a. [2 marks] The functions f and g are defined for x e R by f(x) = 6x2 - 12x + 1 and g(x) = -x + c, where c E R. Find the range of f. 4b. [4 marks] Given that (go f) (x)

a. The functions f and g are defined, for x R, by Find fg(4). b. The functions h and k are defined, for x > 0, by Express each of the following in terms of h and k. i. ii. x x + 8 iii. x x 2 - 4...

The functions f and g are defined for x R by f: x 3x + 2 g: x x + 1 a) Find the values of x for which fg(x) = gf(x). b) Find an expression for (fg) (x), stating its domain. c) Explain why (fg) ...

The functions f and g are defined for x R by f: x x 1 g: x 3x + 4 a) Find and simplify expressions for fg(x) and gf(x). b) Hence find the values of a for which fg(a) = 4a + gf(a).

The functions f and g are defined, for x R, by f: x 3x - k, where k is a positive constant g: x 5x - 14/x+1, where x -1. a. Find expressions for f -1 and g -1 . b. Find the value of k for which f...

Birds Eye View manufactures satellite dishes used in residential and commercial installations for satellite-broadcasted television. For each unit, the following costs apply: $50 for direct material,...

Assuming that the investor wants to hold the property for 5 years, conduct a discounted cash flow analysis (DCF) to calculate the after-tax IRR and NPV for this investment. The investor received a...

A firm has credit sales of $ 8 , 4 0 0 , cost of goods sold of $ 3 , 9 0 0 , inventory of $ 6 0 0 , and accounts receivable of $ 7 0 0 . How is the operating cycle computed? Multiple choice question....

=+It is estimated that the competitive selling price for color laser printers ofthis type will drop to $270 next year. Spectrum Imaging has established a target cost to maintain its historical markup...

For each variable (other than ID), obtain appropriate descriptive statistics (both numeric and graphic)? Table 2.17: Format for FEV.DAT The data in Table 2.17 are available for each child. Variable...

Use both numeric and graphic measures to assess the relationship of FEV to age, height, and smoking status. (Do this separately for boys and girls.) Table 2.17: Format for FEV.DAT The data in Table...

Compare the pattern of growth of FEV by age for boys and girls. Are there any similarities? Any differences? Table 2.17: Format for FEV.DAT The data in Table 2.17 are available for each child....

You have just turned 30 years old, have just received your MBA, and have accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every...

You own a one-year American put option on a stock, with a strike price of $80.00. The stock is not expected to pay dividends over the following year and its current price is $70.00. You know that u =...

EXERCISE 6A-1 High-Low Method LO6-10 The Cheyenne Hotel in Big Sky, Montana, has accumulated records of the total electrical costs of the hotel and the number of occupancy-days over the last year. An...