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official document of baabtra –Mentoring Partner
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3. ALGEBRA
PROBLEMS
Ashwin Anand V
Email:ashwinanand99@gmail.com
Facebook id:ashwinanand99@gmail.com
4. 1) If f(x) = 5 - 2x, then f -1(-3) = ?
a) 3 b) 4
c) 6 d) 8
5. 2) If f(x) = x - 4, then (f o f)(3) = ?
a) 4 b) -3
c) -5 d) -11
6. 3) The number of solutions of (x2 + 1)2 +
2(x2 + 1) - 3 = 0 is equal to ?
a) 1 b) 3
c) 0 d) 2
7. 4) Find the distance between the points (-4 , -5)
and (-1 , -1).
a) 16 b) 5
c) 3 d) 6
10. Solution 1:
Find f -1(x) and then Find f -1(- 3)
y = 5 - 2x , given
x = 5 - 2y , interchange x and y
2y = 5 - x , y = log2(5 - x) , solve for y
f -1(x) = log2(5 - x) , inverse function
f -1(- 3) = log2(5 + 3)
= log2(23) = 3
11. Solution 2 :
If f(x) = x - 4, then (f o f)(3) =
(f o f)(3)
= f(f(3))
= f(3 - 4)
= f(-1)
=-5
12. Solution 3
Let u = x2 + 1 and rewrite the given equation in terms of u as follows
u 2 + 2u - 3 = 0
Factor and solve the above equation
(u + 3)(u - 1) = 0
two solutions: u = x2 + 1 = - 3 and u = x2 + 1 = 1
Equation x2 + 1 = - 3 has no solutions. Solve the equation x2 + 1 = 1
for to get
x = 0.
The given equation has one solution.
13. Solution 4
The distance d between points (-4 , -5) and (-1 , -1) is given by
d = sqrt[ (-1 - -4) 2 + (-1 - -5) 2 ]
Simplify.
d = sqrt(9 + 16) = 5
14. Solution 5
Given the function
f(x) = 6x + 1
f(2) - f(1) is given by.
f(2) - f(1) = (6*2 + 1) - (6*1 + 1) = 6
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