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If the function `f: R to R ` defined by `f(x)=(3^(x)+3^(-x))/(2)`, then S.T `f(x+y)+f(x-y)=2f(x)f(y)`.

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-FUNCTIONS -TEXTUAL EXERCISES (EXERCISE-1 (A)
  1. If the function f is defined by f(x) = {{:(x+2, x gt 1),(2, -1 le x...

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  2. If f: R - {0} to R is defined by f(x) = x^(3)-1/(x^3), then S.T f(x) +...

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  3. If f: R to R is defined by f(x)=(1-x^(2))/(1+x^(2)) then show that f(t...

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  4. If f:R-(pm1)toR is defined by f(x)=log|(1+x)/(1-x)|, then show that f(...

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  5. If A={-2,-1,0,1,2} and f:A to B is a surjection defined by f(x)=x^(2)+...

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  6. If A = {1, 2, 3, 4} and f: A to R is a function defined by f(x) = (x^(...

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  7. If f(x+y)=f(xy)AAx,y in R then prove that f is a constane function.

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  8. If A={x:-1 le x le 1},f(x)=x^(2) and g(x)=x^(3), which of the followin...

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  9. If A = { x : -1 le x le 1}, g(x) = x^(3) , which of the following are...

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  10. Which of the following are one-one ,onto (or) bijections? Justify your...

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  11. f : R to (0, oo) defined by f (x) = 2 ^(x) . then f ^-1(x)

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  12. Determine whether the function f:(o,oo) to R defined by f(x) log(e)x i...

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  13. Determine whether the function f:R to [0,oo) defined by f(x)=x^(2) is ...

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  14. If f:[0,infty) to R defined by f(x) = x^(2), then f is

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  15. f: R to R defined by f (x) = x ^(2). then f^-1(x)

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  16. Is g={(1,1),(2,3),(3,5),(4,7)} is a function from A={1,2,3,4}. to B={1...

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  17. If the function f: R to R defined by f(x)=(3^(x)+3^(-x))/(2), then S....

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  18. If the function f: R to R defined by f(x)=(4^(x))/(4^(x)+2), then show...

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  19. If the function f: { -1, 1} to {0,2}, defined by f(x) = ax+b is a surj...

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  20. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

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