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If f : R rarr R, f(x) = sin^(2) x + cos^...

If f : `R rarr R`, f(x) `= sin^(2) x + cos^(2) x`, then f is

A

One - one but not onto

B

Onto but not one-one

C

Neither one-one nor onto

D

Both one-one and onto

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Assignment (Section - A) Objective Type Questions (one option is correct)
  1. Function f : [(pi)/(2), (3pi)/(2)] rarr [-1, 1], f(x) = sin x is

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  2. Function f[(1)/(2)pi, (3)/(2)pi] rarr [-1, 1], f(x) = cos x is

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  3. If f : R rarr R, f(x) = sin^(2) x + cos^(2) x, then f is

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  4. If function f(x) = (1+2x) has the domain (-(pi)/(2), (pi)/(2)) and co-...

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  5. The function f : (0, oo) rarr [0, oo), f(x) = (x)/(1+x) is

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  6. If f(x) = x/(x-1)=1/y then the value of f(y) is

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  7. gof exists, when :

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  8. If f : R rarr R, f(x) = x^(2) + 2x - 3 and g : R rarr R, g(x) = 3x - 4...

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  9. If f : R rarr R, f(x) = x^(2) - 5x + 4 and g : R^(+) rarr R, g(x) = lo...

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  10. If f : R - {1} rarr R, f(x) = (x-3)/(x+1), then f^(-1) (x) equals

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  11. If function f : R rarr R^(+), f(x) = 2^(x), then f^(-1) (x) will be eq...

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  12. If f(x) = 2 sinx, g(x) = cos^(2) x, then the value of (f+g)((pi)/(3))

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  13. The graph of the function y = log(a) (x + sqrt(x^(2) + 1)) is not sym...

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  14. If the function f:[1,oo)to[1,oo) is defined by f(x)=2^(x(x-1)) then f^...

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  15. Given f(x) = (1)/((1-x)), g(x) = f{f(x)} and h(x) = f{f{f(x)}}, then t...

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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)(x...

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  17. If g(f(x))=|sinx|a n df(g(x))=(sinsqrt(x))^2 , then f(x)=sin^2x ,g(x)...

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  18. Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0)...

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  19. If f : [1, oo) rarr [2, oo) is given by f(x) = x + (1)/(x) then f^(-1)...

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  20. If f : [0, oo) rarr [0, oo) and f(x) = (x^(2))/(1+x^(4)), then f is

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