Answer:
y=42
Step-by-step explanation:
7y = 6×49
y = (6×49)÷7
y= 42
Answer:
- f^-1(x) = (3/8)(x +1) . . . . as written
- f^-1(x) = (x +5)/(3x -1) . . . with appropriate parentheses
Step-by-step explanation:
The inverse function can be found by solving for y:
x = f(y)
x = y + 5/3y -1 . . . . . . . . . . y +(5/3)y -1 . . . per order of operations
x+1 = 8/3y . . . . . . . . . . add 1
(3/8)(x +1) = y . . . . . . . . multiply by 3/8
f^-1(x) = (3/8)(x +1) . . . . . inverse of the function as written
_____
Perhaps you intend f(x) = (x+5)/(3x-1). The inverse is found the same way.
x = (y +5)/(3y -1)
x(3y -1) = y +5
3xy -x = y +5 . . . . . eliminate parentheses
3xy -y = x + 5 . . . . . add x-y
y(3x -1) = x +5 . . . . . factor out y
y = (x +5)/(3x -1) . . . divide by the coefficient of y
f^-1(x) = (x +5)/(3x -1) . . . . inverse of rational function
To simplify the process of expanding a binomial of the type (a+b) n (a + b) n, use Pascal's triangle. The same numbered row in Pascal's triangle will match the power of n that the binomial is being raised to.
A triangular array of binomial coefficients known as Pascal's triangle can be found in algebra, combinatorics, and probability theory. Even though other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy, it is called after the French mathematician Blaise Pascal in a large portion of the Western world. Traditionally, the rows of Pascal's triangle are listed from row =0 at the top (the 0th row). Each row's entries are numbered starting at k=0 on the left and are often staggered in relation to the numbers in the next rows. The triangle could be created in the manner shown below: The top row of the table, row 0, contains one unique nonzero entry.
Learn more about triangle here
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