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Here are two one-to-one functions f (x ) and g ( x ) if
(f o g )( x ) = x AND ( g o f ) ( x ) = x
then we say that f ( x )& g ( x ) are inverses of each other. More particularly we will say that g ( x ) is the inverse of f ( x ) and specified it by
g ( x ) = f -1 ( x )
Similarly we could also say that f ( x ) is the inverse of g ( x )and specified it by
f (x ) = g -1 ( x )
The notation which we use really based upon the problem. In most of the cases either is acceptable.
For the two functions which we started off this section along with we could write either of the following two sets of notation.
f ( x ) = 3x - 2 f -1(x) = x /3+ 2/3
g ( x ) = x/3 + 2/3 g -1 (x ) = 3x - 2
Now, be careful along with the notation for inverses. The "-1" is not an exponent in spite of the fact that is certain does look like one! While dealing with inverse functions we've got to keep in mind that
f-1(x) ≠ 1/ f ( x )
(8x^3+6x^2-8x-15)+(4x-5)
Sketch the graph of function. f ( x ) =3x + 6 /x -1 Solution Thus, we'll start off with the intercepts. The y-intercept is, f (0) =6/-1=-6⇒ (0, -6)
5x+3y=0
xifx+6=33..
How did they get an answer of 4.24899(-6) the question isc=4d(-1)/3.b. I now i substitute 23,245 for d and 13.5 for b, but don''t understand how they got this answer?
In this section we're going to revisit some of the applications which we saw in the Linear Applications section & see some instance which will require us to solve a quadratic equat
Solve x =√(x+ 6) . Solution In this equation the fundamental problem is the square root. If it weren't there we could do the problem. The whole procedure that we're going
1/1+x+1/y+1/1+z+1/x+1/1+y+1/z=1
What type of equation is used if a ball is thrown upward 1.63 meters off the ground and it reaches 3.34 meters in height at 0.6 seconds before falling to the ground?
#If the common factor is known how do you find what the entire equation be (ex: A varies directly with t^2; A=8 when t=2. What is the formula?)
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