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Maths inverse question

g(x)=ax+b

Given that g–1(x)= g(x), show that a=-1 for all values of x.

I made the equation x-b/a= ax+b and fiddled around with the equation, but I'm not sure how to get a. Thank you in advance.
Original post by BenJohnson
g(x)=ax+b

Given that g–1(x)= g(x), show that a=-1 for all values of x.

I made the equation x-b/a= ax+b and fiddled around with the equation, but I'm not sure how to get a. Thank you in advance.


Compare coefficients.

The coefficient of xx on the LHS must be the same as the one on the RHS. Therefore we get 1a=a\dfrac{1}{a} = a.

Similarly, the constant coefficient must also be balanced, so −ba=b-\dfrac{b}{a} = b.
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BenJohnson
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Original post by RDKGames
Compare coefficients.

The coefficient of xx on the LHS must be the same as the one on the RHS. Therefore we get 1a=a\dfrac{1}{a} = a.

Similarly, the constant coefficient must also be balanced, so −ba=b-\dfrac{b}{a} = b.

Thank you :smile:

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