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Consider the function `f(x)={2x+3, x le 1 and -x^2+6, x > 1` Then draw the graph of the function `y=f(x), y=f(|x|), y=|f(x)|, and y=|f(x)|.`

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CENGAGE-RELATIONS AND FUNCTIONS-Solved Examples And Exercises
  1. Consider the function f(x)={2x+3, x le 1 and -x^2+6, x > 1 Then draw t...

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  2. Find the inverse of the function: f:(-oo,1] rarr [1/2,oo],w h e r ef(...

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  3. Find the value of x for which function are identical. f(x)=xa n dg(x)=...

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  4. Find the value of x for which function are identical. f(x)=cosxa n dg(...

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  5. Find the value of x for which function are identical. f(x)=(sqrt(9-x^2...

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  6. Find the inverse of the function: f: R rarr (-oo,1)gi v e nb yf(x)=1-...

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  7. f:(2,3)vec(0,1)d efin e db yf(x)=x-[x],w h e r e[dot] represents the g...

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  8. Find the inverse of the function: f(x)={x^3-1, ,x<2x^2+3,xgeq2

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  9. Find the inverse of the function: f:[-1,1]rarr[-1,1]defined byf(x)=x|...

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  10. If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,d e t e ...

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  11. Let f(x)=(9^x)/(9^x+3) . Show f(x)+f(1-x)=1 and, hence, evaluate. f(1/...

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  12. If f(x+2a)=f(x-2a),t h e np rov et h a tf(x)i sp e r iod i cdot

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  13. Let g(x) be a function such that g(a+b)=g(a)dotg(b)AAa , b in Rdot If...

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  14. Find the value of x for which function are identical. f(x)=tan^(-1)x+t...

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  15. The period of f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x , where n in ...

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  16. Plot y=|x|,y=|x-2|, and y=|x+2|

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  17. If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is ...

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  18. If for all real values of ua n dv ,2f(u)cosv=(u+v)+f(u-v), prove that ...

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  19. If the period of (cos(sin(n x)))/(tan(x/n)),n in N ,i s6pi , then n= ...

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  20. If f: X rarr[1,oo) is a function defined as f(x)=1+3x^3, find the su...

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  21. Find the period (if periodic) of the following function ([.] denotes ...

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