# How To Solve Inverse Questions Quickly

## 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

$f^{-1} = \frac{1}{2} (5^x + 1)$

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)

### 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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