Inverse of a function y=4x-3,y=2/(x-5) Example-1

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Home > Algebra calculators > Inverse of a function example

3. Inverse of a function example ( Enter your problem )

( Enter your problem )

y=4x-3 $y=4x-3$ ,y=2x-5 $y=2/(x-5)$ Example-1
y=x2+4 $y=x^2+4$ ,y=x-4x+4 $y=(x-4)/(x+4)$ Example-2

Other related methods

2. Range of a function
(Previous method)

y=x2+4 $y=x^2+4$ ,

y=x-4x+4 $y=(x-4)/(x+4)$ Example-2
(Next example)

1. y=4x-3 $y=4x-3$ ,y=2x-5 $y=2/(x-5)$ Example-1

1. y=4x-3 $y=4x-3$ , find Inverse of a function

Solution:

y=4x-3 $y=4x-3$

Replace all x with y and y with x.

x=4y-3 $x=4y-3$

Now, Solve

x=4y-3 $x=4y-3$ for y

Interchange sides

⇒4y-3=x $=>4y-3=x$

⇒4y=x+3 $=>4y=x+3$

⇒y=x+34 $=>y=(x+3)/4$

2.y=2x-5 $y=2/(x-5)$ , find Inverse of a function

Solution:

y=2x-5 $y=2/(x-5)$

Replace all x with y and y with x.

x=2y-5 $x=2/(y-5)$

Now, Solve

x=2y-5 $x=2/(y-5)$ for y

Interchange sides

⇒2y-5=x $=>2/(y-5)=x$

⇒y-52=1x $=>(y-5)/2=1/(x)$

⇒(y-5)=1x×2 $=>(y-5)=1/x xx 2$

⇒y-5=2x $=>y-5=2/x$

⇒y=2x+5 $=>y=2/x+5$

This material is intended as a summary. Use your textbook for detail explanation.
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