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How do you find the inverse of #g(x)=5x-2#?

Answer 1

Sadie Ackerman

#g^-1(x)=(x+2)/5#

#"let "y=5x-2#

#"rearrange making x the subject"#

#5x=y+2#

#x=(y+2)/5#

#rArrg^-1(x)=(x+2)/5#

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Answer 2

Lily Anderson

To find the inverse of the function g(x) = 5x - 2, you follow these steps:

Replace g(x) with y.
Swap x and y to get x in terms of y.
Solve the resulting equation for y.
Replace y with the inverse function notation, usually denoted as g^(-1)(x).

So, for g(x) = 5x - 2:

Replace g(x) with y: ( y = 5x - 2 ).
Swap x and y: ( x = 5y - 2 ).
Solve for y: [ x = 5y - 2 ] [ x + 2 = 5y ] [ \frac{x + 2}{5} = y ]
Replace y with the inverse function notation: ( g^{-1}(x) = \frac{x + 2}{5} ).

Therefore, the inverse function of g(x) = 5x - 2 is ( g^{-1}(x) = \frac{x + 2}{5} ).

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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.