Inverse Problem & Function(x) Problems

[snakeyesxlaw]

Problem#1: Let f(x)= (14 x + 19) / (x - 15)

Then f^(-1)(x) = (Ax + B) / (Cx + D)

where A, B, C, D are integers with A positive and the fraction cannot be reduced.

okay so basically, i started this:

x(y - 15) = 14y + 19
xy - 15y = 14y + 19
xy = 14y + 19 + 15y
xy = 29y + 19

x = (29y + 19) / y

what next? any suggestions?

Problem #2: The product of a number and the square of another number is 62.5. If x is the number that is squared, write the sum S of the two numbers as a function of the number x.

S(x) =

okay, so far:

y(x^2) = 62.5

 

[skeeter]

Problem#1: Let f(x)= (14 x + 19) / (x - 15)

Then f^(-1)(x) = (Ax + B) / (Cx + D)

where A, B, C, D are integers with A positive and the fraction cannot be reduced.

okay so basically, i started this:

x(y - 15) = 14y + 19
xy - 15y = 14y + 19

first mistake in the line above ...

x(y - 15) = 14y + 19
xy - 15x = 14y + 19

now solve for y.

Problem #2: The product of a number and the square of another number is 62.5. If x is the number that is squared, write the sum S of the two numbers as a function of the number x.

S(x) =

okay, so far:

y(x^2) = 62.5

the sum of the two numbers is S = x + y

if y(x^2) = 62.5, then y = ?

 

[snakeyesxlaw]

Problem#1: Let f(x)= (14 x + 19) / (x - 15)....

x(y - 15) = 14y + 19
xy - 15x = 14y + 19

now solve for y.

okay, so i solve for y and get:

y= (xy - 15x - 19) / 14

but for some reason that does not seem correct.. stuck there..

Problem #2: The product of a number and the square of another number is 62.5. If x is the number that is squared, write the sum S of the two numbers as a function of the number x.

the sum of the two numbers is S = x + y

if y(x^2) = 62.5, then y = ?

okay so then:
y = s - x

which would then give:

(s - x) * (x^2) = 62.5

s = (62.5 / x^2) + x

stuck here..

 

[stapel]

okay, so i solve for y and get:

y= (xy - 15x - 19) / 14

But this isn't solve "for y". You still have a "y" on the right-hand side. Try getting all the y-containing terms on one side of the "equals" sign, with all the other terms on the other side, Then factor out the y, and divide off whatever is left. This should give you "y=" in terms only of x.

okay so then: y = s - x

Where is "s" coming from? Why are you finding a difference, instead of a sum?

Instead, try working from the exercise and the set-up provided. The exercise states, and you were given, that:

. . . . .y x² = 62.5

Solve this for "y=". Then find the sum, S, of y and x, but in terms only of x.

Eliz.

 

[snakeyesxlaw]

thanx for the concepts!

got 'em right!