Question

If f : R → R is defined by f(x) = 2X-3. Rrove that f is a bijection and find its inverse.

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Answer 1

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I do the two halves of your question in reverse order:

f doubles its argument and then subtracts 3.

Its inverse must do the opposite tasks in the opposite order. In other words, it adds 3 and then halves. Writing this in mathematical symbols: f^1(x) = (x+3)/2.

The fact that we have managed to find an inverse for f means that f is a bijection.

Hope it helps uh!!

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Answer 2

Answer:

f:R→R,2x2−7∀x∈R

For each values of x there is a unique value of f and no x∈Ris left and f∈R which do not have a image and preimage respectively.

⇒f is one-one.

⇒f is onto.

⇒f is bijective.

Step-by-step explanation:

f:R→R,2x2−7∀x∈R

For each values of x there is a unique value of f and no x∈Ris left and f∈R which do not have a image and preimage respectively.

⇒f is one-one.

⇒f is onto.

⇒f is bijective.