f:R+ [9,infinity]
f(x)=5x2+6x-9.
Prove that f is invertible
USING COMPLETING SQUARE METHOD ONLY

Dear Student,
Please find below the solution to the asked query:

Given:f:R+-9,   it should be -9-9, is called co-domain of fxfx=5x2+6x-9since domain is R+, x0f'x=10x+6 since x>0, f'x>0, hence the function is increasing or one-one.now range of function will be:since function is increasing in 0,, we can saylowest value will be at x=0hence,fx=0+0-9=-9hence range for R+ is -9,since range = co-domain the function is onto.Hence it is invertible:now by completing square method:fx=5x2+6x-9=5x2+6x5-95=5x2+2.x.35+925-95-925    adding and subtracting 925y=5x2+2.x.35+352-5425y=5x+352-545hence,y+545=5x+352y5+5425=x+352x+35=±y5+5425x=-35±y5+5425since x>0we will take only:x=-35+y5+54255x=-3+5y+54   ans 

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards

  • 29
What are you looking for?