Find the Inverse of the following functions f X 3 X 7 fX

Find the Inverse of the following functions: f (X) = 3 X - 7 f(X) = f(X) = f(X) = f(X) Y is directly proportional to X (or Y varies as X). If X = 5 then Y = 12. Determine the Constant of proportionality k. When X = 10 find the Value of Y. Y is directly proportional to X and inversely proportional to t. X = - 2and t = 4 then Y = 7. Find the Constant of proportionality k. Find all values of X such that f(X) >0 and find all values of X such that f(X)

Solution

5)

let f(x)=y

=>x=f^-1(y)

now

i)

f(x)=3x -7

3x-7=y

=>x=(y+7)_/3

=>f^-1(y)=(y+7)_/3

=>f^-1(x)=(x+7)_/3

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ii)

f(x)=2_/(x+1)

2_/(x+1)=y

=>x+1=2_/y

=>x=(2-y)_/y

=>f^-1(y)=(2-y)_/y

=>f^-1(x)=(2-x)_/x

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iii)

f(x)=3x_/(x-2)

3x_/(x-2)=y

=>(x-2)_/3x=1_/y

=>(1_/3)-(2_/3x)=1_/y

=>(1_/3)-(1_/y)=(2_/3x)

=>(2_/3x)=((y-3)_/3y)

=>(1_/x)=((y-3)_/2y)

=>x=2y_/(y-3)

=>f^-1(y)=2y_/(y-3)

=>f^-1(x)=2x_/(x-3)

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iv)

f(x)=x³ -6

x³ -6=y

=>x³=(y+6)

=>x=(y+6)^1/3

=>f^-1(y)=(y+6)^1/3

=>f^-1(x)=(x+6)^1/3

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v)

f(x)=-x³ +2

-x³+2=y

=>x³=(2-y)

=>x=(2-y)^1/3

=>f^-1(y)=(2-y)^1/3

=>f^-1(x)=(2-x)^1/3

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