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How to Solve Inverse Question Quickly in Aptitude
Here , In this Page How to Solve Inverse Questions Quickly is given.Inverse functions has Many importance in Aptitude.It is also used in Geometry.
For a function to have an inverse, the function has to be 1 to 1. That means every output only has one input.
Inverse questions are basically of 2 types.
- Algebraic Questions
- Geometric Questions
In Algebraic Questions Algebra is involved whereas In Geometric Questions Trigonometry is involved.


Types 1. Algebraic Questions
Question 1 Find an equation for the inverse of the function given f(x) = 3x + 2
Options
A f-1(x) = \frac{1}{3} \ (x-2)
B f-1(x) = \frac{1}{2} \ (x-2)
C f-1(x) = \frac{3}{2} \ (3x-2)
D f-1(x) = \frac{1}{2} \ (2x-1)
Explanations
First we drop the function notation and write y instead of f(x). Then we solve for x and finally, swap x and y.
y = 3x+2
swap x and y
x = 3y+2
3y = x-2 (divide by 3)
\frac{x-2}{3} \ = y
f-1(x) = \frac{1}{3} \ (x-2)
Correct Options (A)
Question 2 f(x) = \frac{x+4}{3x – 5}
Options
A f-1(x) = \frac{5x+4}{3x-1} \
B f-1(x) = \frac{5x+3}{3x-1} \
C f-1(x) = \frac{2x+3}{5x-1} \
D None of these
Explanations
First we drop the function notation and write y instead of f(x). Then swap x and y.
y = \frac{x+4}{3x-5}
x = \frac{y+4}{3y-5} (multiply by 3y-5)
x(3y-5) = y+4 (distribute)
3xy – 5x = y+4 (add 5x, subtract y)
3xy – y = 5x +4 (factor out y)
y(3x – 1) = 5x + 4 (divide by 3y – 1).
y = \frac{5x+4}{3x-1} \
f-1 (x)= \frac{5x+4}{3x-1} \
Correct option (A)
Question 3 f(x) = log _5 (2x-1)
Options
A f^{-1} = \frac{1}{2} (5^x + 1)
B f^{-1} = \frac{2}{5} (2^x + 1)
C f^{-1} = \frac{3}{5} (x+ 1)
D None of these
Explanations
y = log _5 (2x-1) (re-write it as exponential statement.
5^{y} = 2x – 1Swap x and y
5^{x} = 2y – 1(add 1)
5^{x} + 1 = 2y (divide by 2)
\frac{5^x + 1}{2} \ = y
y = \frac{1}{2}(5^x + 1)
f-1 = \frac{1}{2} (5^x + 1)
Correct Options (A)
Types 2. Geometric Questions
Question 1 What is the inverse function of tan(x)?
Options
A cos^{-1}(x)
B tan^{-1}(x)
C tan^{-1}(\frac{1}{x})
D None
Solution
y = tan(x)x = tan(y)
y = tan^{-1}(x)
Correct Option B
Question 2 What is the value of sin(sin^{-1}(x)) where x belongs to [-1,1]
Options
A 1
B 0
C x
D None
Solution
In this Expression sin(sin^{-1}(x))
Domain of sin^{-1}(x) is [-1,1] so it's value will be x
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