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Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.?

source : yahoo.com

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.?

1)

You need to put parenthesis in your question. Did you mean g(x) = (-3x-7)/(x-1)?

f(x) = (x-7) /(x+3)

f(g(x)) = f [ (-3x-7) /(x-1)]

Replace x with (-3x-7)/(x-1) in f

Evaluate (-3x-7)/(x-1) by replacing x with (x-7)/(x+3)

evaluate the numerator (-3x-7):

– 3 (x-7)/(x+3) -7 = (-3x+21)/(x+3) – 7

= [(-3x+21) -(7x+21)] /(x+3) = (-3x+21-7x-21)/(x+3) = -10x/(x+3) ——(1)

evaluate the denominator (x+3)

(-3x-7) /(x+3) +3

= [ (-3x-7) + 3(x-1)] /(x+3) = (-3x-7+3x-3)/(x+3) =-10/(x+3) ——–(2)

(1)/(2) = -10x/-10 = x

We have shown that f(g(x)) = x

————————————————–

g(x) = [(-3x-7) /(x-1)]

numerator of g(f(x)) = [ -3( (x-7)/(x+3) – 7] = [-3x+21-7(x+3)]/(x-1) = (-3x+21-7x-21)/(x-1) = -10x/(x-1)

denominator of g(f(x)) = (x-7)/(x+3)-1 = ((x-7)-x-3)/(x-1) = -10/(x-1)

divide = -10x/(x-1)/-10/(x-1) = x

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

——————————————————————————-

2)

cos 4x +cos 2x = 2 cos ^2 2x -1 + 2 cos^2 x -1

= 2(1 – sin^2 2x ) -1 +cos 2x

=1-2sin^2 2x + 1-2sin^2 x

=2 – 2sin^2 2x – 2 sin^2 x

=

How do you show that f(x)=(x-1)/(x+5) and g(x)=-(5x+1)/(x

How do you show that f(x)=(x-1)/(x+5) and g(x)=-(5x+1)/(x – If two functions f(x) and g(x) are inverses, then they will be reflections of each other over the line y=x (shown in green). It's clear to see that f(x) and g(x) are reflections of each other over the line! Precalculus . Science Anatomy & Physiology Astronomy AstrophysicsTo give you two different examples, let f and g be functions defined as follows: f(x)=x + 5/6. g(y)=6y – 5 (I took the liberty of using y in the definition for g) Then you verify as follows: g(f(x)) = g(x + 5/6) = 6(x + 5/6)-5 = 6x + 5 – 5 = 6x. In this case, f and g are not inverses of each other. Now, if you were to find that g(f(x)) = x, youso, the first thing the question asks of you is to see that f(g(x)) = x. try it out, plugging g(x) in as the x-variable in the first equation: f(g(x)) = (∛(x – 4))³ + 4 they were merciful in writing this problem, and thankfully your cube roots cancel out and don't cause you any trouble. continue solving:

How would I confirm that f and g are inverses by showing – If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector . College Algebra! help! Consider the following functions f(x)= (7x+8)/(x+3) and g(x)= (3x-8)/(7-x) (a) Find g(g(x)) (b) Find g(f(x)) (c) Determine whether the functions f and g are inversesBecause f ∘g(x) ≠ x, we don't have to find g ∘f(x). So, f(x) and g(x) are inverse to each other. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here."g of f of x," or g(f(x)) = (2x + 8/x -1) + 8/(2x + 8/x – 1) – 2. you also need to prove that this equals out to x and therefor the two functions are inverses. Im sorry i worked on this for a bit trying to get the algebra of it down, but cant seem to get it.

How would I confirm that f and g are inverses by showing

Confirm that f and g are inverses by showing that f(g(x – If functions f(x) and g(x) are inverses, their compositions will equal x. Composition 1: f(g(x)) f(g(x)) = ((2x – 3) + 3)/2 = (2x)/2 = x" "color(greenClick here 👆 to get an answer to your question ️ Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. MEE1Esaracouriali MEE1Esaracouriali 07/19/2016 Mathematics High SchoolQED Graphically, 2 functions are inverses if they are symmetric with respect to the line y=x graph{(y-3+4x)(4y-3+x)(y-x)=00 [-3.7, 4.095, -0.95, 2.945]} Precalculus Science

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