If f ( 5 − x x − 3 ) = x − 2 3 x − 2 , find f ( 1 ) .
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Check your arithmetic men.
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I believe it's right
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Thanks Sir Lakshya Sinha for your response.
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@Brian Dela Torre – sir you are elder than me and please don't call me sir, it's embarrassing :-). BTW I got the problem wrong.
I prefer an alternative means. We rewrote the original equation to f ( − 1 + 5 − x 2 ) = 3 + x − 2 4 Let y = − 1 + 5 − x 2 . Rewrote it to x = 5 − 2 y + 1 , then plug in y to the LHS and x to the RHS. This will give f ( y ) = 3 + 5 − y 8 ⇒ f ( x ) = 3 + 5 − x 8 = 5 − x 2 3 − 3 x Here, just plug in x = 1 and the answer will be f ( 1 ) = 3 + 5 − 1 8 = 3 + 2 = 5
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In f( 5 − x x − 3 ), we want to make this function into f(1)
Thus, solving the problem we have to equate 5 − x x − 3 = 1, and we get x = 4
Then substituting thus value of x in the expression x + 1 3 x − 2 , we have
x − 2 3 x − 2 = ( 4 ) − 2 3 ( 4 ) − 2 = 5
Hence the answer is 5