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Show that f(x) = loga x "on" (0,oo ),(a ...

Show that `f(x) = log_a x "on" (0,oo ),(a gt 0 "and" a != 1)` functions are injective.

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`f(x)=log_a x[1,oo]`
` "for" alpha,beta in [1, oo]`
`"Let" f(alpha)=f(beta) `
`implieslog_a alpha = log_alpha beta implies alpha = beta `
`:." F is one -to one".`
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MBD PUBLICATION-RELATION AND FUNCTION-QUESTION BANK
  1. Show that f(x)=sin x on [0, pi/2] functions are injective.

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  2. Show thatf(x)= cos x [0 , pi] functions are injective.

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  3. Show that f(x) = loga x "on" (0,oo ),(a gt 0 "and" a != 1) functions a...

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  4. Show that f(x)=a^x "on" R.(a gt 0 "and" a != 1) functions are injectiv...

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  5. Show that functions f and g defined by f(x)=2 log x and g(x)=log x^2 a...

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  6. Give an example of a function which is Surjective but not injective.

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  7. Give an example of a function which is injective but not surjective.

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  8. Give an example of a function which is neither injective nor surjectiv...

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  9. Give an example of a function which is bijective

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  10. Prove that {1,2,3,4,5,6,……} set are equivalent.

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  11. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  12. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  13. Prove that the following sets are equivalent {1, 2, 3, 4, 5, 6.....}...

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  14. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  15. Let f= {(1,3),(2,4),(3,7)} and g ={(3,2),(4,3),(7,1)} Determine gof ...

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  16. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domains of f and g.

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  17. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2. Compute fog and gof and find th...

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  18. "Let" f(x) =sqrtx "and" g(x) = 1 -x^2.Find natural domain of h(x) = 1-...

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  19. Let f(x) = sqrt(x) and g(x) = 1 -x^(2). Show that hgof only on R(0)=...

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  20. Find the composition fog and gof and test whether fog = gof when f and...

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