Question

Find the inverses of the following functions

1. f(x)s=-4x+5 2.

2.f(x)= 7x/ (6x-5)

3. g(x) = √(x-7)

Answer 1

1)

f(x)=-4x+52.

y =-4x+52

4x = 52-y

x = (52-y)/4

f^-1(x) =(52-x)/4

Thus f inverse of x is (52-x)/4

-------------------

2)

f(x)=7x/ (6x-5)

y =7x/ (6x-5)

(6x-5)y =7x

6xy-5y =7x

6xy-7x=5y

x(6y-7)=5y

x=5y/(6y-7)

f^-1(x) =5x/(6x-7)

Thus f inverse of x is 5x/(6x-7)

------------------------------

3)

g(x)=√(x-7)

y =√(x-7)

y^2 =x-7

x=y^2+7

f^-1(x) =x^2+7

Thus f inverse of x is x^2+7