If f(x)=2 x+3 and g(x)=3 x-1 then find f^-1 og^-1 (1) (x+8)/(6) (2) (x-8)/(6) (3) (8-x)/(6) (4)

Name: Problem 47, Chapter 6: The IIT Foundation series of Mathematics Class
Uploaded: 2021-08-01T00:08:22-08:00
Duration: 1 min 40 s
Channel: Saurabh Chandra
Description: If f(x)=2 x+3 and g(x)=3 x-1 then find f^-1 og^-1 (1) (x+8)/(6) (2) (x-8)/(6) (3) (8-x)/(6) (4) (x-8)/(2)

step 1 Hello students in this problem function f x is given to be 2x plus 3 and g x function is given a

Question

If $f(x)=2 x+3$ and $g(x)=3 x-1$ then find $f^{-1} \operatorname{og}^{-1}$ (1) $\frac{x+8}{6}$ (2) $\frac{x-8}{6}$ (3) $\frac{8-x}{6}$ (4) $\frac{x-8}{2}$

   If $f(x)=2 x+3$ and $g(x)=3 x-1$ then find $f^{-1} \operatorname{og}^{-1}$
(1) $\frac{x+8}{6}$
(2) $\frac{x-8}{6}$
(3) $\frac{8-x}{6}$
(4) $\frac{x-8}{2}$

The IIT Foundation series of Mathematics Class

Trishna Knowledge… 5th Edition

Chapter 6, Problem 47

Instant Answer

Solved by Expert Saurabh Chandra

08/01/2021

Step 1

Step 1: Given the functions $f(x)=2x+3$ and $g(x)=3x-1$, we need to find $f^{-1} \circ g^{-1}$. Show more…

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If $f(x)=2 x+3$ and $g(x)=3 x-1$ then find $f^{-1} \operatorname{og}^{-1}$ (1) $\frac{x+8}{6}$ (2) $\frac{x-8}{6}$ (3) $\frac{8-x}{6}$ (4) $\frac{x-8}{2}$

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Key Concepts

Inverse Function

An inverse function reverses the effect of the original function, meaning that if a function f takes an input x to an output y, then its inverse f?¹ will take y back to x. This is characterized by the relationship f(f?¹(x)) = x and f?¹(f(x)) = x.

Finding Inverses of Functions

Finding the inverse of a function involves interchanging the dependent and independent variables and then solving the resulting equation to express the original input in terms of the output. This process is especially straightforward for linear functions, where algebraic manipulation quickly yields the inverse.

Composite Functions

Composite functions involve applying one function to the outcome of another function. When dealing with the composition of inverse functions, the output of one inverse function is used as the input to another, requiring careful attention to the order of operations to ensure accurate results.

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