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PREPINSTA PRIME
How To Solve Inverse Questions Quickly
How to Solve Inverse Question Quickly in Aptitude
Here , In this Page you will find, How to Solve Inverse Questions Quickly. 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. In Algebraic Questions Algebra is involved whereas In Geometric Questions Trigonometry is involved.
How to solve Inverse function
Inverse Rational Function
A rational function is a function of form f(x) = P(x)/Q(x) where Q(x) ≠ 0. To find the inverse of a rational function, follow the following steps.
- Step 1: Replace f(x) = y
- Step 2: Interchange x and y
- Step 3: Solve for y in terms of x
- Step 4: Replace y with f-1(x) and the inverse of the function is obtained.
Inverse Questions and Answers
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 : Find the inverse of 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 3x – 1).
y = \frac{5x+4}{3x-1} \
f-1 (x)= \frac{5x+4}{3x-1} \
Correct option (A)
Question 3 : Find the inverse of 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 – 1
Swap 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)
Question 4 : 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 5: 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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- HCF and LCM – Questions Formulas | How to Solve Quickly | Tricks & Shortcuts
- Number Decimals & Fractions – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Surds and Indices – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Divisibility – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Ages – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- LCM – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- HCF – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Inverse – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- HCF and LCM –
Questions
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Number System –
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How to Solve Quickly |
Tricks & Shortcuts - Number Decimals & Fractions –
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Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Surds and Indices-
Questions |
Formulas |
How to Solve Quickly |
Tricks & Shortcuts - Divisibility –
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How to Solve Quickly |
Tricks & Shortcuts - Ages –
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How to Solve Quickly |
Tricks & Shortcuts
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