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Show that a^(x)+a^(-x) is an even functi...

Show that `a^(x)+a^(-x)` is an even function.

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To show that the function \( f(x) = a^x + a^{-x} \) is an even function, we need to demonstrate that \( f(-x) = f(x) \). ### Step-by-Step Solution: 1. **Define the function**: Let \( f(x) = a^x + a^{-x} \). 2. **Find \( f(-x) \)**: ...
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RESONANCE ENGLISH-RELATION, FUNCTION & ITF-SSP
  1. Show that a^(x)+a^(-x) is an even function.

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  2. If (2x+y,7)=(5,y-3) then find x and y

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  3. If AxxB={(1,2),(1,3),(1,6),(7,2),(7,3),(7,6)} then find sets A and B.

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  4. If A={x,y,z} and B={1,2}, then the number of relations from A to B is

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  5. Write R={(4x+3,1-x):xle2,xepsilonN}

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  6. Let L be the set of all lines in a plane and let R be a relation defin...

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  7. Let R be a relation on the set of all lines in a plane defined by (...

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  8. Let g(x) be a function defined on[-1,1]dot If the area of the equilate...

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  9. Represent all possible functions from {alpha, beta} to {1,2}.

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  10. Find the domain of following function: f(x)=1/(log(2-x))+sqrt(x+1)

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  11. Find the domain of following function: f(x)=sqrt(1-x)-"sin^(-1)((2x-1)...

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  12. Find domain and range of following function: y=x^(3)

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  13. Find domain and range of following function: y=(x^(2)-2x+5)/(x^(2)+2x+...

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  14. Find domain and range of following function: y=1/(sqrt(x^(2)-x))

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  15. Following each of the following function find whether it is one-one o...

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  16. Examine whether the following functions are one-one, many-one or into,...

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  17. Examine whether the following functions are one-one, many-one or into,...

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  18. Examine whether the folloiwng pair of function are identical or not: f...

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  19. Examine whether the folloiwng pair of function are identical or not: f...

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  20. Define fog(x) and gof(x). Also find their domain and range. (i) f(x) =...

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  21. Define fog(x) and gof(x). Also find their domain and range. f(x) = tan...

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