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What is the inverse function of #y=2x-1#?

Answer 1

Lily Anderson

The inverse function is #y = (x+1)/2 #

Firstly, switch the x and the y:

# y = 2x-1 => x = 2y-1 #

Now, solve for y:

# x = 2y -1 #

Add 1 to both sides:

# x+1 = 2y cancel(-1) cancel(+1) #

#x+1 = 2y#

And divide by 2:

#(x+1)/2 = cancel(2)y/cancel(2)#

#(x+1)/2 = y#

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Answer 2

Christian Antunez

To find the inverse function of ( y = 2x - 1 ), we switch the roles of ( x ) and ( y ) and then solve for ( y ).

So, if ( y = 2x - 1 ), we first swap ( x ) and ( y ) to get: [ x = 2y - 1 ]

Next, solve this equation for ( y ): [ x = 2y - 1 ] [ x + 1 = 2y ] [ \frac{x + 1}{2} = y ]

Therefore, the inverse function is: [ f^{-1}(x) = \frac{x + 1}{2} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.