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Mock Test-1 Functions, Full Marks-10, Cut Off-07

This mock test covers functions and their properties. It contains 10 questions testing concepts like defining functions, finding domains and ranges, plotting graphs of functions, function composition, odd and even functions, and solving equations involving functions. The test is out of 10 total marks and a score of 7 or higher is needed to pass.

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ud54
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77 views1 page

Mock Test-1 Functions, Full Marks-10, Cut Off-07

This mock test covers functions and their properties. It contains 10 questions testing concepts like defining functions, finding domains and ranges, plotting graphs of functions, function composition, odd and even functions, and solving equations involving functions. The test is out of 10 total marks and a score of 7 or higher is needed to pass.

Uploaded by

ud54
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Mock Test-1

Functions, Full Marks- 10, Cut off-07


1. Given are two sets A {1, 2, -2, 3} and B = {1, 2, 3, 5}. Is the function f(x) =
2x - 1 defined from A to B?
2. Find the range and domain of the function f(x) = (2x+1)/(x-1) and also find
its inverse.
3. Find domain and range of the function f(x) = (x2+2x+3)/(x2-3x+2)
4. Find the period of following functions
(a) cos3x + sin 5x
(b) |cos x| + |sin2x|
(c) x - |x|.
5. If graph of function f(x) is as shown in the figure given below, then plot the
graph of |f(x)|, f(x) + 1, f(x + 2) and f-1 (x)

6. If f(x) = 1 + x; 0≤x≤2
=3 - x; 2 < x ≤3

Determine

(a) g(x) = f(f(x)) (b) f(f(f(x)))


(c) f([x])

7. If f(x) = ((1-x)/(1+x)) x ≠ 1 and x ɛ R.


8. Then show that
(i) f(1/x) = -f(x), x ≠ 0
(ii) f(f(x)) + f(f(1/x)) ≥ 2 for x > 0.

9. Show that if an odd function is invertible, then its inverse is also an odd
function.
2 2
10. Solve (x) = [x] + 2x

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