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How do you find the inverse of #f(x)=3x-5#?

Answer 1

#f(x)^-1 =1/3x+5/3#

#f(x)=3x-5# The inverse of a function completely swaps the x and y values. One way to find the inverse of a function is to switch the "x" and "y" in a equation #y=3x-5# turns into #x=3y-5# Then solve the equation for y #x=3y-5# #x+5=3y# #1/3x+5/3=y# #f(x)^-1 =1/3x+5/3#

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Answer 2

Caleb Alexander

#f(x)=3x-5#

#y=3x-5#

#x=3y-5#

add three to both sides

#3y=x+5#

divide by #three# on both sides

#f^-1(x)#=#5/3# + #x/3#

#f^-1(x)#=#x+5# /#3#

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Answer 3

Chloe Alexander

To find the inverse of ( f(x) = 3x - 5 ), follow these steps:

Replace ( f(x) ) with ( y ): ( y = 3x - 5 ).
Swap the variables ( x ) and ( y ): ( x = 3y - 5 ).
Solve the equation for ( y ).
Add 5 to both sides: ( x + 5 = 3y ).
Divide both sides by 3: ( \frac{x + 5}{3} = y ) or ( y = \frac{x + 5}{3} ).

So, the inverse of ( f(x) = 3x - 5 ) is ( f^{-1}(x) = \frac{x + 5}{3} ).

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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.