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In electrical circuit theory, a circuit C(t) called a linear circuit if it satisfies the superposition principle given by `C(at_(1)+bt_(2))=aC(t_(1))+bC(t_(2))`, where a, b are constants. Show that the circuits `C(t)=3t` is linear.

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PREMIERS PUBLISHERS-RELATIONS AND FUNCTION -EXERCISE 1.5
  1. Using the functions f and given below ,find f^(@) g and g^(@) f, Check...

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  2. Using the function f and g given below, find the fog and gof. Check wh...

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  3. Using the function f and g given below, find the fog and gof. Check wh...

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  4. If f(x)=3+x, g(x)=x-4, then check whether fog=gof.

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  5. Using the function f and g given below, find the fog and gof. Check wh...

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  6. Find the value of k, such that fog=gof f(x)=3x+2, g(x)=6x-k

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  7. Find the value of k, such that fog=gof f(x)=2x-k, g(x)=4x+5

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  8. If f(x)=2x-1, g(x)=(x+1)/(2), show that fog=gof=x.

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  9. If f(x)=x^(2)-1, g(x)=x-2 find a, if gof(a)=1.

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  10. Find k, if f(k)=2k-1 and fof(k)=5.

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  11. Let A, B, C in N and a function f:A to B be defined by f(x)=2x+1 and g...

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  12. Let f(x) =x^(2) -1 Find f^(@) f (ii) f^(@) f^(@) f

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  13. If f: R to R and g: R to R are defined by f(x)=x^(5) and g(x)=x^(4) th...

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  14. Consider the function f(x) , g(x) ,h(x) as given below , Show that (f...

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  15. Consider the function f(x), g(x), h(x) as given below. Show that (fog)...

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  16. Consider the function f(x), g(x), h(x) as given below. Show that (fog)...

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  17. Let f={(-1, 3}, (0, -1), (2, -9)} be linear function from Z into Z. Fi...

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  18. In electrical circuit theory, a circuit C(t) called a linear circuit i...

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