Question

Let the function f and g be defined as f(x) = x/ x − 1 and...

Let the function f and g be defined as f(x) = x/ x − 1 and g(x) = 2 /x +1 . Compute the sum (f + g)(x) and the quotient (f/g)(x) in simplest form and describe their domains.

(f + g )(x) =

Domain of (f+g)(x):

(f/g)(x) =

Domain of (f/g)(x):

Math   Precalculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Given f(x) = x / (x-1) and g(x) = 2 / (x+1)

Then f+g(x) = f(x) + g(x)

Thus, f+g(x) = [ x/(x-1) ] + [ 2/(x+1) ]

f+g(x) = [ x(x+1) + 2(x-1) ] / (x-1)(x+1)

f+g(x) = [ x2 + x +2x - 1 ] / (x2 - 12)

f+g(x) = ( x2 +3x -1 ) / (x2 -1)

Hence, f+g(x) = [ x2 +3x -1 ] / [ x2 -1 ]

f+g(x) is not defined when the denominator is zero

Thus, (x+1)(x-1) ≠ 0 implies x ≠ 1 , -1

Domain of f+g(x) is  (- , -1 ) U ( -1 , 1 ) U ( 1 , )

f/g (x) = f(x) / g(x)

Thus, f/g(x) = [ x / (x-1) ] / [2 / (x+1) ]

= [ x / (x-1) ] × [ (x+1) / 2 ]

= x(x+1) / 2(x-1)

= ( x2 + x ) / (2x -2)

Hence f/g (x) = [ x2 +x ] / [ 2x -2 ]

f/g (x) is not defined when the denominator is zero

Thus, 2x-2 ≠ 0

Thus, 2x ≠ 2 implies x ≠1

Domain is ( - , 1 ) U ( 1 , )

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
a.)Consider the function f (x) = 3x/ x^2 +1 i) Evaluate f (x+1), and f (x)+1....
a.)Consider the function f (x) = 3x/ x^2 +1 i) Evaluate f (x+1), and f (x)+1. Explain the difference. Do the same for f (2x) and 2f (x). ii) Sketch y = f (x) on the interval [−2, 2]. iii) Solve the equations f (x) = 1.2 and f (x) = 2. In each case, if a solution does not exist, explain. iv) What is the domain of f (x)? b.)Let f (x) = √x −1 and g (x) =...
Let f : [0,∞) → [0,∞) be defined by, f(x) := √ x for all x...
Let f : [0,∞) → [0,∞) be defined by, f(x) := √ x for all x ∈ [0,∞), g : [0,∞) → R be defined by, g(x) := √ x for all x ∈ [0,∞) and h : [0,∞) → [0,∞) be defined by h(x) := x 2 for each x ∈ [0,∞). For each of the following (i) state whether the function is defined - if it is then; (ii) state its domain; (iii) state its codomain; (iv) state...
Let f, g : Z → Z be defined as follows: ? f(x) = {x +...
Let f, g : Z → Z be defined as follows: ? f(x) = {x + 1 if x is odd; x - 1 if x is even}, g(x) = {x - 1 if x is odd; x + 1 if x is even}. Describe the functions fg and gf. Then compute the orders of f, g, fg, and gf.
Let g(x) = 25e^.04x Write the inverse of g and specify its domain. Let f(x) =...
Let g(x) = 25e^.04x Write the inverse of g and specify its domain. Let f(x) = -7x + 12. Compute and simplify the difference quotient given by (f(x+h)-f(x))/h. In triangle ABC side a =10in., side b = 5in., and∠60 degrees . Find the length of side c. (Leave your answer in radical form.) If sin x = -4/7 and x is an angle in Quadrant III, find the value of tan x. Find the value of Arcsin(− 3/2).
Let f: Z→Z be the functon defined by f(x)=x+1. Prove that f is a permutation of...
Let f: Z→Z be the functon defined by f(x)=x+1. Prove that f is a permutation of the set of integers. Let g be the permutation (1 2 4 8 16 32). Compute fgf−1.
Let the function f be defined by y= f (x), where x and f (x) are...
Let the function f be defined by y= f (x), where x and f (x) are real numbers. Find f (2), f (-3), f (k), and f (k^2-1) f(x) = 2/3 x + 5
Let f, g : X −→ C denote continuous functions from the open subset X of...
Let f, g : X −→ C denote continuous functions from the open subset X of C. Use the properties of limits given in section 16 to verify the following: (a) The sum f+g is a continuous function. (b) The product fg is a continuous function. (c) The quotient f/g is a continuous function, provided g(z) != 0 holds for all z ∈ X.
Let f: [0, 1] --> R be defined by f(x) := x. Show that f is...
Let f: [0, 1] --> R be defined by f(x) := x. Show that f is in Riemann integration interval [0, 1] and compute the integral from 0 to 1 of the function f using both the definition of the integral and Riemann (Darboux) sums.
f(x)=1x−2 and g(x)=x−7x+3. For each function h given below, find a formula for h(x) and the...
f(x)=1x−2 and g(x)=x−7x+3. For each function h given below, find a formula for h(x) and the domain of h. Use interval notation for entering the domains. a) h(x)=(f∘g)(x). h(x) = Domain = b) h(x)=(g∘f)(x). h(x) = Domain = c) h(x)=(f∘f)(x). h(x) = Domain = d) h(x)=(g∘g)(x). h(x) = Domain =
1. Let f be the function defined by f(x) = x 2 on the positive real...
1. Let f be the function defined by f(x) = x 2 on the positive real numbers. Find the equation of the line tangent to the graph of f at the point (3, 9). 2. Graph the reflection of the graph of f and the line tangent to the graph of f at the point (3, 9) about the line y = x. I really need help on number 2!!!! It's urgent!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT