• This is an assessment test.
      • To draw maximum benefit, study the concepts for the topic concerned.
      • Kindly take the tests in this series with a pre-defined schedule.

Algebra: Functions Test-1

Congratulations - you have completed Algebra: Functions Test-1.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%
Your answers are highlighted below.
Question 1
If md (x) = I x I, mn (x, y) = minimum of x and y and Ma (a, b, c, ....) = maximum of a, b, c, ... Value of Ma [md (a),mn (md (b), a), mn (ab,md (ac))] where a = - 2, b = - 3, c = 4 is
A
2
B
6
C
8
D
-2
Question 1 Explanation: 
Ma [md (a),mn (md (b), a), mn (ab,md (ac))]
Segregating the individual terms inside the third bracket:
i) md(a) =|a|. In this case as a=-2 and md(a)=2
ii)md (ac)= md|-2 x 4|= 8 using a = - 2, c = 4
iii) mn((ab,md (ac)) = mn(6,8)=6
iv) mn (md (b), a) =mn (3,-2) =-2. Ma [md (a),mn (md (b), a), mn (ab,md (ac))] =[2,-2,6] =6
Question 2
If it is given  that a >b  and if md (x) = I x I, mn (x, y) = minimum of x and y and Ma (a, b, c, ....) = maximum of a, b, c, ..., then the relation Ma [md (a) mn (a, b)]=mn [a,md (Ma (a, b))] does not hold if
A
a< 0, b < 0,
B
a> 0, b > 0
C
a> 0, b < 0, I a I < I b I
D
a> 0, b < 0, I a I > I b I
Question 2 Explanation: 
Segregating and simplifying:
Considering a>b,
ma [md (a), b)]=mn [a,md (a)]
Now, whether a is greater than zero or less than zero won’t affect md (a)=|a|.
Then, ma(|a|,b) will not be equal to mn [a,md (a)] if a<0,
Only one option has a<0.
Question 3
f(x) = 2x +3 and g(x) = (x -3)/2 then,fog (x)=
A
1
B
gof(x)
C
$ \displaystyle \frac{15x+9}{16x-5}$
D
$ \displaystyle \frac{1}{x}$
Question 3 Explanation: 
f(x) = 2x +3, g(x) = (x -3)/2
fog(x)=2{(x -3)/2}+ 3 =x-3+3 =x
gof(x)=(2x+3-3)/2=x
Therefore correct option is (b)
Alternatively,
it can be easily observed that g(x)=f-1(x)
Therefore, fog(x)=gof(x)
Question 4
f(x) = 2x +3 and g(x) = (x -3)/2 then For what value of x; f (x) = g (x - 3)
A
- 3
B
1/4
C
-4
D
None of these
Question 4 Explanation: 
g(x) = (x -3)/2
=>g(x-3) = (x -3-3)/2 =(x-6)/2
Therefore 2x+3 =(x-6)/2
Solving for x we will get x=-4.
Question 5
f(x) = 2x +3 and g(x) = (x -3)/2 thenWhat is value of (gofofogogof) (x) (fogofog)(x)
A
x
B
x2
C
$ \displaystyle \frac{5x+3}{4x-1}$
D
$ \displaystyle \frac{\left( x+3 \right)\,\left( 5x+3 \right)}{\left( 4x-5 \right)\,\left( 4x-1 \right)}$
Question 5 Explanation: 
g(x)=f-1(x),
fog(x)=x and gof(x)=0
Therefore,
(gofofogogof) (x) (fog)(x)
=(gofofog) (x) (fog)(x)
=(x) (gof) (x) =x2
Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results
There are 5 questions to complete.
List
Return
Shaded items are complete.
12345
End
Return

Want to explore more Arithmetic Tests?

Explore Our Arithmetic Tests

Website Pop Up
https://forms.gle/BJ7YdM5c3HM6N3XQA

FREE CHEAT SHEET

Learn
How to Master VA-RC 

This free (and highly detailed) cheat sheet will give you strategies to help you grow

No thanks, I don't want it.

Join our Free TELEGRAM GROUP for exclusive content and updates

Rsz 1rsz Close Img

Join Our Newsletter

Get the latest updates from our side, including offers and free live updates, on email.

Rsz Undraw Envelope N8lc Smal
Rsz 1rsz Close Img