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Show that the function f: RvecR given by...

Show that the function `f: RvecR` given by `f(x)=cosxfora l lx in R ,` is neither one-one nor onto

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We have,
`f: R, f(x)=cos x`
Now,
`f(x_{1})=f(x_{2}) `
` cos x_{1}=cos x_{2} `
` ...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
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  7. Show that f: RvecR , given by f(x)=x-[x], is neither one-one nor onto.

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  9. If f(x)=e^x and g(x)=(log)e x(x >0), find foga n dgofdot Is fog=gof?

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  12. If f(x)=sqrtx(x > 0) and g(x)=x^2-1 are two real functions, find fog a...

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  16. If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4)=1, then (gof)...

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