If f: R →R defined by f(x)=3 x-5, then f^-1({-1,-2,1,2})= (1) {1, (4)/(3), (7)/(3)} (2) {-1,2, (

Name: Problem 43, Chapter 6: The IIT Foundation series of Mathematics Class
Uploaded: 2021-08-01T00:07:29-08:00
Duration: 1 min 46 s
Channel: Saurabh Chandra
Description: If f: R →R defined by f(x)=3 x-5, then f^-1({-1,-2,1,2})= (1) {1, (4)/(3), (7)/(3)} (2) {-1,2, (-4)/(3)} (3) {1,2, (4)/(3), (7)/(3)} (4) {1,2,-1,-2}

step 1 Hello students in this question a function fx is defined as 3x minus 5 and we have to find the p

Question

If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ defined by $\mathrm{f}(\mathrm{x})=3 \mathrm{x}-5$, then $\mathrm{f}^{-1}(\{-1,-2,1,2\})=$ (1) $\left\{1, \frac{4}{3}, \frac{7}{3}\right\}$ (2) $\left\{-1,2, \frac{-4}{3}\right\}$ (3) $\left\{1,2, \frac{4}{3}, \frac{7}{3}\right\}$ (4) $\{1,2,-1,-2\}$

   If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ defined by $\mathrm{f}(\mathrm{x})=3 \mathrm{x}-5$, then $\mathrm{f}^{-1}(\{-1,-2,1,2\})=$
(1) $\left\{1, \frac{4}{3}, \frac{7}{3}\right\}$
(2) $\left\{-1,2, \frac{-4}{3}\right\}$
(3) $\left\{1,2, \frac{4}{3}, \frac{7}{3}\right\}$
(4) $\{1,2,-1,-2\}$

The IIT Foundation series of Mathematics Class

Trishna Knowledge… 5th Edition

Chapter 6, Problem 43

Instant Answer

Solved by Expert Saurabh Chandra

08/01/2021

Step 1

Step 1: We are given a function $f(x) = 3x - 5$ and we are asked to find the inverse images of the set $\{-1, -2, 1, 2\}$ under this function. Show more…

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If $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ defined by $\mathrm{f}(\mathrm{x})=3 \mathrm{x}-5$, then $\mathrm{f}^{-1}(\{-1,-2,1,2\})=$ (1) $\left\{1, \frac{4}{3}, \frac{7}{3}\right\}$ (2) $\left\{-1,2, \frac{-4}{3}\right\}$ (3) $\left\{1,2, \frac{4}{3}, \frac{7}{3}\right\}$ (4) $\{1,2,-1,-2\}$

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Key Concepts

Inverse Function

An inverse function reverses the mapping of the original function: if a function f sends x to y, then its inverse f?¹ sends y back to x. This concept is fundamental in understanding how to retrieve original inputs when given outputs.

Preimage

The preimage under a function is the set of all elements from the domain that map to elements of a given subset in the codomain. Determining the preimage requires solving equations to find which inputs correspond to the specified outputs.

Linear Functions

Linear functions, expressed in the form f(x) = ax + b where a ? 0, describe relationships with a constant rate of change. Their simplicity makes them a common subject for studying function inverses and preimages.

Solving Linear Equations

Solving linear equations involves finding the value of the variable that satisfies equations of the first degree. This process is key when computing inverse functions for linear mappings by isolating the variable.

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