How To Solve Inverse Questions Quickly

How to Solve Inverse Question Quickly:-

Inverse functions gives lots of troubles so here’s a quick run down of what an inverse function is, and how to find it.

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

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)

(e) None of these

Correct Options (A)

Explanations

First we drop the function notation and write y instead off(x). Then we solve for x and finally, swap x and y.

y= 3x+2 (subtract 2)
3x = y-2  (divide by 3)
\frac{y-2}{3} \ = x
swap  x and y
f-1(x) = \frac{1}{3} \ (x-2)

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

Correct option (A)

Explanations

First we drop the function notation and write y instead off(x). Then we solve for x and finally, swap x and y.

y = \frac{x+4}{3x-5} \    (multiply by 3x-5)
y(3x-5) = x+4   (distribute)
3xy – 5y = x+4   (add 5y, subtract x)
3xy – x = 5y +4  (factor out x)
x(3y – 1) = 5y + 4  (divide by 3y – 1).

x = \frac{5y+4}{3y-1} \
swap x and y

y = \frac{5x+4}{3x-1} \

f-1 (x)= \frac{5x+4}{3x-1} \

How To Solve Quickly Inverse Questions.

Question 3

f(x) = log _5 (2x-1)

Options

(a) f-1 = \frac{1}{2} \ (5x+ 1)

(b) f-1 = \frac{2}{5} \ (2x+ 1)

(c) f-1 = \frac{3}{5} \ (x+ 1)

(d) None of these

Correct Options (A)

Explanations

y = log _5 (2x-1)   (re-write it as exponential statement.

5y = 2x – 1 (add 1)
5y + 1 = 2x (divide by 2)
\frac{5^y + 1}{2} \ = x  (swap x and y)
y = \frac{1}{2} \ (log x + 1)
f-1 = \frac{1}{2} \ (5x+ 1)

Read Also: Formula for Inverse Question

how to solve inverse questions quickly

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